Transcript for:
Understanding Lines and Angles in Geometry

Hello everyone welcome to magnet brains I am Abhishek Kumar We have come with a new chapter today The name of the chapter is Lines and Angles This is chapter number 5 in your NCRT book So children pay attention that in the 6th class we have learned about lines What are lines? When I mark a dot on a plane using a pen I will not pick up the pen when I extend the dot in any direction in any direction and I will not pick up the pen then from there that dot is used and that point is a line When I extend the segment, I get the line. Here, pay attention, what is written on the slide in front of you?

Here it is written, a line segment. What is the word? The word is line segment. So what is the meaning of line segment word? There are two end points of it.

When I say a word line alone, then in the sixth class we heard this word line. I just told you the meaning of line. You want to extend the dot and don't pick up the pen.

So the line extends to any end. A dot is getting extended. So the number of dots make the line.

You have also heard the word line segment in the sixth class. There are two end points of the line segment. So the first point is written.

Line segment has two end points. If you see the drawing, you can see the line segment here. There are two endpoints of this line segment. One is point P and the other is point Q.

It is clear. In the next point, I have written, when we extend the two endpoints. When I extend both these endpoints, that means If you see this drawing, when I extend these two endpoints, I mean, I extend and make an arrow on both the ends. When I Extend the line segment and make an arrow.

In any direction, we get a line. This is called a line. This line goes on.

In any direction, the word I have used, it will be drawn in any direction. If you want it in both, then this arrow means this. So this is the line and this is the line segment.

PQ is known as a line segment because it has two endpoints. And in this case, A and B are not endpoints. From here two arrows will be formed and the line will be pulled. So when to use the word line and when to use the word line segment, we should know this. Next, a line has no end points.

The line does not have any end points. Like if you see here O, a line. If I make an arrow from P here, then it is called Ray. It will go in any direction. So it is going in any one direction.

When there is one end point and in other we go in any direction. So for this we use word R. When is line used? When is the word line used?

Segment Segment means measured line Segment means measured line Segment means measured line Segment means In the 7th class, we will learn about the angle formations of the lines. Along with that, we will learn about the relationship between angles. So, you have to understand this.

And angle, what is angle? You have also studied this in 6th class. Angle is formed when lines and line segments meet.

Means, when lines, see these are lines, there is an arrow at both ends. So, when lines, two lines or more than two lines meet, this is the center point, when they meet, at which point they are meeting, angles are formed at that point. These are the angles. This is an angle.

What is the name of angle? POS and you had learnt in 6th class that if we are saying angle POS so in this drawing angle POS means the center O is an angle on O so always remember the center is written the center is written here we say an angle is formed either we call it angle POS or we call it angle O When I talk about this angle, then this angle will be angle ROQ. Angle ROQ. O will always be in the center because an angle is forming here. Similarly, if I see that there is a line segment here.

A is a line segment. A is a line segment. B is a line segment. This is a line segment, so line segment is the angle formation.

See, A and C, these two line segments meet here. So, an angle formed here and this is angle A. Either we call it angle A or angle BA or angle C. So, you have to understand that whenever you will tell the name of angles in this chapter, the small mistakes where teacher does half marks cutting, she will do cutting here.

Some children, if I ask angle BA, tell this angle. If I ask them, tell this angle. So, some children come with wrong angle.

They say, sir, this is angle C. No. When you talk about angle C, A, B, then A is written in the center. And the thing which is in the center, the angle formation is there. So I asked you this angle, you are telling me this angle, then teacher marks cut here.

Take care of this thing. If I have asked this angle, then angle C will come in the center. And its angle is like this. what will be in the next and next side?

here and here here will be A and B so A will come ahead and here will be B here will be angle AB here will be angle BA this is similar angle So, in the center there is C, which means I am talking about angle C. These are some small things which we understood in class 6th. In 7th class we have to keep these things in mind because most of the mistakes are going to be made here. Next, we understand what to do.

Now, here you will get to see some words and those words are very good words. Words like here are complementary angles. A word is complimentary word c o m p l e complimentary when I talk about word complimentary what does complimentary mean?

It means the sum of the measure of two angles is 90 degree means any two angles sum will be 90 degree bhi 2 angles ka sum 90 degree hoga. Ye hota hai complementary angles. Word complementary apni copy me likh lo. Tk kyunki ab aapko yehi words is chapter me use karne hai. Tk.

Complementary angles when the sum of the measure of 2 angles is 90 degree the angles are called complementary angles. Ab baat ko samjo ki main bol raha hu yeh ek angle hai. Aur yeh angle hai mera around 40 degree.

And I have one more angle and this angle is 50 degree. Now understand the thing, 40 plus 50 gives me 90. So I will say that these two angles are complementary angles and complementary angles are made inside one angle like this. If this is made 90 degree.

So the sum of the two angles inside it will always be complementary. When you add 40 and 50, the angle will be 90 degrees. Always remember to show 90. Two straight lines and a box type is made in the middle. This way an angle type is made.

This is not a curve. Here, there is a rectangle formation inside. So, this is 90 degree.

And the sum of two angles will be 90 degree. For that, we will use word complementary angle. So, you should know this thing. Let's see the next slide. What is complementary?

Note this. I have written this definition in front of you. Okay. I am telling you next word is supplementary angles What are supplementary angles?

One is complementary which you understood in the back Second is supplementary Write this word in the heading What does supplementary angles mean? When sum of two angles Means this is an angle 60 degree And here is an angle 120 degree When I will sum of two angles So 180 degree should come in the sum What was in the back? 90 degree sum karne pe 90 degree aana chahiye supplementary me sum karne pe 180 degree aana chahiye the sum of the measures of the angles in each of the above pair comes out to be 180 degree yeh cheez aap notice kar paare hoge dekho 60 plus 120 to 60 plus 120 karunga 180 aayega aise hi yaha pe me 68 plus 180 to If I do 112, then you will notice that 180 is coming.

So, the first figure has two angles. The second figure has two angles. So, when two angles are in between, Match, sum, right?

So, this sum should always be 180 degree. This is the principle of supplementary. Ok. So, what is the definition of supplementary?

Sum of both the angles is 180 degree. Complementary which we have read in the back. What does that mean?

The sum of two angles is 90 degree. Read further. Such pairs of angles are called supplementary angles.

These two angles. We will say that these two are supplementary in each other. Ok.

What is the relation between these two in each other? Supplementary angles. Ok.

Ok. Two angles are supplementary, each angle is said to be the supplement of the other. How do you say this? If someone asks you, what is the relation of You will say that this is the supplement angle of Word Supplement angle You can highlight this in your copy and write it Under this topic, this thing should be highlighted If you want to tell the relation of one angle to another Then how do we say in mathematics We will say 68 degree is supplement to 112 degree Or 112 degree is supplement to 68 degree Similarly here 60 degree is supplement to 120 degree 120 degree is supplement to 60 degree So word supplement means sum of both 180 degree Clear? So you understood two things here What is complementary angle and what is supplementary angle Let's understand further Next, understand, here you will get to hear one more word, that is adjacent angles.

Adjacent angles, word adjacent means in English dictionary, the one next to you. Absolutely next to you, adjacent. Adjacent to you, the one sitting next to you, that is what we are talking about. So when I talk about adjacent angles, So, when an angle is formed, as explained in the drawing of NCIT, here an angle is formed, this is the center point and this angle is formed. So, what is the adjacent of this angle?

This is the adjacent of this angle. This was the center point. And, What is the adjacent of this angle?

This is the adjacent of this angle. Can I say that all three angles are adjacent? Adjacent angle means this is adjacent.

Similarly, they have given you a book drawing in NCERT. Here also, they have given the adjacent angle. If I turn the pages of this point, the center point of the book, where binding is there, if I consider it as a vertex in top view, and this angle will form here and this angle will form here.

Hold it for 2 minutes. If I assume a point here, then one point will form here and one angle will form here. So, this angle, can I say that this angle has an adjacent?

Adjacent means that the next angle is adjacent. So, that is what I have explained to you. Our vertices A and B of the angles are placed next to each other. In both the drawings, which are given in NCNT.

These angles are such that they have a common vertex. Whenever I have placed the adjacent angle, So, this point where all the angles meet, we call that angle as vertex angle. So, this will be a common vertex.

Understand this, if I am saying that this is an angle and the angle of this angle is This is the vertex, I have drawn a line like this. A line segment. I have drawn a line segment like this.

I have drawn a line segment like this. So, what is the adjacent angle of this angle? Commonly, on a similar vertex, Angle is made on this vertex, this angle is also made on this vertex, this angle is also made on this vertex and this angle is also made on this vertex.

So, when number of angles are there on the same vertex, then we say for that, They have a common arm. Their arm is also common. Now, what does it mean that the arm is common? When I say adjacent angle, then you have to pay attention here.

If I talk about this angle in this drawing, if I talk about this angle in this drawing, this angle, then what is the adjacent of this angle? This means there is a common arm in it. This is a common arm. Now what is arm?

What is arm? You have done sixth. You have done sixth. class where I have studied.

In angles, if I talk about any angle, then there is a vertex inside the angle. This is a vertex. This is a vertex. and both of these hands arm means hands in English so for these we use word in mathematics in angle that these are arms so it is saying that there should be a common arm so I will call that angle as adjacent angle So, this is adjacent and this is not.

When will it be adjacent? When it is attached together. If it is here and if we use this line, then it will be adjacent. If I draw a line here, then this angle and this angle are common arms.

This should be a common arm. We call the same angle as an adjacent angle. Okay, third understanding the non common arms are on either side of the common arm.

Now one point is going to give more attention to this. It is a common thing. If I say that there is an adjacent angle, like this case here, this angle is And it is like this here.

So, there are three angle formations. One, one and one. Now this is common arm, so this angle is adjacent to this angle. This angle is adjacent to this angle. This angle is adjacent to this angle.

I will say adjacent means the angle next to it. What is important to note in this is that the arms outside will not stick together. They will be outside. There will be only one common arm which is mentioned in the second point.

The non-common arms, these are the non-common arms. This one and this one. These are the non-common arms. They are on either side of the common arm. They are on both the sides of the common arm.

Okay, this is what is mentioned in the third point. So, you should understand the meaning of adjacent angles. We have read three things till now. What is a complementary angle?

What is a supplementary angle? What are adjacent angles? The type of We have completed three angles till this slide.

Let's see further. What is given next? The word Linear Pair In this chapter, you will get to hear this word a lot The word is Linear Pair Linear Pair means The word Linear A Linear Pair is a pair of Adjacent Angles We have understood what are Adjacent Angles Adjacent Angles are the ones which stick together and have common arm Okay If There are two adjacent angles.

So, what will be the linear pair whose non-common sides are opposite rays? Means, what is he trying to say? Understand this thing. Here I drew a straight line.

I have drawn a line on this straight line. The ray that I have drawn here, there are two adjacent angles here. I will say angle 1 is adjacent to angle 2. Is angle 1 adjacent to angle 2?

If angle 1 is adjacent to angle 2, then the thing to be noted here is that the common arm is the one that is adjacent to the angle 1 and angle 2. The non-adjacent arm is the one that is adjacent to the angle 1 and angle 2. Common side was there, which non-common side? This is a straight line. When I sum these two angles on this straight line, then this sum should always be 180 degrees. Means, we have read complementary and supplementary.

So, sum of two angles is 180 degree. And linear pair is called as INI. Linear pair means, when two adjacent angles join on one common line. If you see the drawing here, then you will see that angle 1 is adjacent to angle 2. But this is not linear pair formation. This is not linear pair.

This is linear pair. So, you should know the meaning of linear pair. Linear means straight line. Line means straight. So, on one common line, when two adjacent angle formations are formed, like this drawing is visible and this is not.

Is it clear, children? So, this is called linear pair. Let's see in the next slide. In linear pair, you have to keep in mind that the angles in a linear pair are supplementary.

I just told you in the back. Now pair of supplementary angles form a linear pair. It is the same thing that supplementary pairs are...

When they meet each other, they form a linear pair. When placed adjacent to each other. When both the angles are placed adjacent to each other. Now understand my point.

Here, first I will explain the drawing later. What I have written here, understand this. I am telling you that there is one angle here.

And this angle is 40 degree. Okay. And the second angle is here.

2 minutes Second angle is like this and this angle is 140 degree Now, in which relation these two angles are in? I will say that 40 degree angle is supplement of 140 degree and 140 degree angle is in which relation? 40 degree because the combination of these two is 180 degree. So when to use supplement word, that is understood.

When to use word linear pair, when I put these two angles adjacent to each other, means this arm is straight and the arm below is also straight. If I extend this arm to this side, then this is 140 degree and this angle will be 40 degree. The thing you can see in the drawing, we can see this in most common houses.

We use this tool to cut vegetables. The knife is placed on the center point. So at this point, if you see the angle from here to here is adjacent to each other and this is on a common line.

So there is a common base of both. When the non common side of both of them meet each other, then a common side is formed. A common side is formed here and a common side is formed here.

So this formation is called linear pair. Like this is a pen stand. You must have seen that pen stands are placed on the table. Base is placed and we put a pen on it. So this is a pen stand.

This point in this pen stand is a vertex. An angle is forming here. So this angle when...

If I keep this angle in adjacent If I keep it in adjacent Then here the formation of 180 degree will be total Because on straight line There is 180 degree angle We have learnt this in 6th class If I consider this point as straight line And if I start moving from here While counting then I will reach here 90 If I come here before 90 then it becomes 180 degree So you should know when to say linear pair When to say supplementary For supplementary angles linear pair both are adjacent to each other and on one common base like I have shown you in the back drawing see that drawing once more this is common base line and here is an angle so here the sum of both is 180 degree in this case the sum of both is not 180 degree first thing so these are not supplementary angles And this is not a straight line, this is not a linear pair. It is clear, children. So, here, that is why I was trying to explain this to you.

Understand further. And what is it? Now you will get to hear one more word Vertically Opposite Angles So till now what all we have completed We have completed Complimentary, Supplementary After Complimentary and Supplementary we have seen Linear Pairs Now we are coming to Vertically Opposite Angles What was the meaning of Vertically Opposite Angles?

Opposite means opposite Now, what does Vertically Opposite Angle mean? If you take two pencils and tie them together with rubber bands, as you can see in the drawing, if I tie two pencils with rubber bands, then you will get one common point. and this will be a common vertex here one angle is here and other angle is here this angle is adjacent to this angle this angle is adjacent to this angle so this angle has two adjacent angles when I use the word Vertically Opposite Angle Opposite means opposite opposite angle if i talk about this angle which angle? this angle so which is the opposite angle of this angle and which is vertical also means vertically opposite means if i stand like this then opposite is opposite so this angle has vertically opposite angle and always remember that the vertical and opposite angles are equal next take two pencils and tie them with a help of a rubber band in a middle as shown this is what I have shown in the drawing see here you are getting four angles angle 1, angle 2, angle 3, angle 4 this is angle 1, angle 2 angle 3 and angle 4. We got 4 angles. Angle 1, angle 2, angle 3 and angle 4. Now, angle 1 is vertically opposite to angle 3. Angle 1 is vertically opposite to angle 3. I just explained this.

And angle 4 is vertically opposite to angle 2. This is what I have written here. Angle 1 is vertically opposite to angle 3 and angle 2 is vertically opposite to angle 4. We call angle 1 and angle 3 a pair of vertically opposite angles. If you see any drawing and...

So, I asked you that tell me which are the pairs of vertically opposite angles. So, how will you tell by looking at it? You will say angle 1 and angle 3. Angle 1, angle 3 are the pair.

is the pair of vertically opposite angle and angle 2 is vertically opposite to angle 4. That means the pair is angle 2 angle 4 and angle 1 angle 3. This is what I have explained to you. Note this. After this we will understand what is next.

Next is Pairs of lines. Now pairs of lines means when lines meet each other, we will learn some things, we will learn some words. basic is seventh class me yeah I put some words introduced cry a jar I take a higher classes may any words can use can come questions we solve carrying it okay so I'm both the chaser buddy here I have a seventh class me cheese you go some Joe a world up a boss Sunniko me Lego word a intersecting lines intersect Intersecting means to intersect with each other When one line intersects with another line, it is called point vertex These are intersecting lines If you see the formation, it is a Y and here a Y is being formed means these 3 lines are forming a Y so I will say 2 lines L and M intersect if they have a point in common first thing if I say there are 2 lines one is line L and other is line M so L and M are intersecting each other if they have a common point of If there is a point which is common Is this thing clear to you? So this common point is called as intersecting point This common point O Means if I give this point name O This common point O is their point of intersection I will call this as point of intersection Is it clear? Write this So after copying this I will tell you one more thing drawing box.

See, there are some lines in it. These lines, can you see these lines? These lines are cutting a line.

Which line is that? These lines. So we will say that the point of intersection is the intersection point And here we will say that this is an intersecting line One line intersecting another line Here also if you see this line It is not intersecting, it is joining here. This is a common vertex, but it is not intersecting.

In this case, it is intersecting. This is called intersection. and the drawing that I have shown here, in this case these are not intersecting lines so this is called as vertex and not intersection if I see it like this, this line is coming and this line is coming and this line is coming and both of them are touching each other then I will say that if they are touching point O by coming in different lines So this is the point of intersection. Is it clear, kids? So till here, you guys understood what is the meaning of intersecting of lines word.

So by combining pairs of lines, you got to hear the word intersecting lines. Secondly, under this topic, If you see the next thing, then you will get to see that transverse transverse transverse transverse means that when a line is going straight, I mean, I am saying this line is and if someone cuts one line from this line then that line cutting line is called line of transversal so you will get to see this thing here like you must have seen many fencing so these fencing blocks are used to join these three blocks together for this we used one more wood here which we have intersected with the help of the nails. When one line cuts three lines, this line is called transversal. A line that intersects two or more lines at distinct points is called a transversal. Distinct means different.

Different points means the line which is cutting these lines Cutting points will be different This is cutting here, this is cutting here, this is cutting here, this is cutting here Cutting is happening at distinct point Okay So A line which cuts two lines, this cutting line is called transversal line. Here you will get to learn many things and this is your main topic. So, pairs of lines together means transversal. So, I am teaching you in the heading of this topic that what is transversal? And after transversal, the basic thing of this chapter starts where the children start getting confused.

So, as soon as you get the word transversal, the only thing that comes to your mind is that some lines were in regular parallel to each other. parallel use kar raha hu 6th class 5th class mein aapko word parallel ka matla bataya tha jaisa ki rail ki patri agar ek patri sidi sidi chal rahi hai uske opposite mein jo dosi patri chalti hai wo kabhi aapas mein meet nahi karti hai tk to parallel hoti hai jab do line aapas mein ek dose ke agal bagal chalti hai aur wo If we don't meet anywhere at any end, if this line doesn't go in like this, if it is going straight, then we will say that these are parallel lines. These are parallel lines.

This line and this line are in parallel. It is going from its side but not meeting. When a line cuts these parallel lines, then we call this cutting line a transversal line. You have to understand these things here. After this, when you read the transversal, you will see that the angle is forming here.

This angle is being formed, this angle is being formed, this angle is being formed, this angle is being formed here. So here you see that two lines were parallel to each other. It is cutting one line. As it is cutting, you will see that many angles are being formed here. This angle, this angle, angle here, angle here.

Do it! When a scenario is created where a parallel line is cut into a line which is called a transversal line So the angles that are created there are the names of those angles I am explaining those names to you next Stay with me in this video You will get to hear many names here You will see what are those names First of all, I will explain you the drawing There are two lines Sir, you said that we should cut the first line. No.

I am saying that when someone cuts two lines, then this line... P is the transversal line. Line P is transversal which is cutting line L and M. Here you will see angles are being made. Here angle 1 is given, angle 2 is given, angle 3 is given, angle 4 is given.

When transversal cut this upper line at this point, then see the cutting point is different. One point is here and one point is here. At this cutting point you are getting 4 angles and at this cutting point you are getting 4 angles Every angle has its own name Listen to this carefully What are interior angles and what are exterior angles? what are interior angles first of all you have learnt interior and exterior in 6th class interior wordy means inner angles exterior means outer angles if you look carefully then what are interior angles And what are exterior angles? So what are exterior angles?

Those which are outside, like angle 1, angle 2, angle 7, angle 8 All these angles are outside, so these are called exterior angles what are the interior angles? Angle 3, angle 4, angle 5 and angle 6 these are the interior angles see what are the interior angles Angle 3, angle 4, angle 5, angle 6 see the interior angles Angle 3, angle 4, angle 5, angle 6 interior angles are inside exterior angles are outside Angle 1, Angle 2, Angle 7, Angle 8 8 note this thing along with it is very important thing because here there should not be confusion further pay attention to pair of corresponding angles now sir you have not told the word corresponding angles yet what is the meaning of corresponding angles what is the meaning of corresponding angles if you look at the drawing carefully then inside this angle 5 and angle 1 look at it when you I will do it again, it will be clear. Pay attention, this angle is angle 1 and angle 5. If I just make nothing here, then you can see a line L here and a line M here.

When this M is cutting the transversal, then this line which is in exterior, means this angle formation is happening at this point. And the angle formation happening here, This angle is called corresponding angles. It means, the angles that look the same.

It means, the common line is cutting two different lines. So, here is the exterior angle and here is the exterior angle. If I remove this upper line, If I remove this line, then you will see that if this is just a line, some transversal is cutting, then this angle also looks like this.

ok, is it looking like this in the picture so this angle will be called corresponding angle angle 1 and angle 5 are corresponding angle angle 2 and angle 6 are corresponding angle angle of so you can say angle to angle 6 they go yeah we see side way when I have you see side webinar yeah we is line K who per side webinar hey yeah it's line K who per side webinar so easily I'm going to angle to Angle 2 and angle 6 are corresponding. Okay. Similarly, angle 7 and angle 3 will also be corresponding angles. Because if you look carefully, then this line going and this line going, if we translate it, is cutting the transversal, so angle 3 is below, this line's cutting line angle is below, similarly this angle is below, so we will call it corresponding angles. So what are pair of corresponding angles?

Angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, angle 4 and angle 8. Note this point very well Angle 4 and Angle 8 are corresponding angles So you should know this word That when to use word corresponding Next is pair of alternate interior angles Alternate means the angle next to each other And here pay attention to word alternate interior interior angles con con said angle 3 angle 4 angle 5 angle 6 drawing me the key angle 3 angle 4 angle 5 angle 6 year interior angle day up is me say alternate interior angles con con say hey alternate world car nice or alternate woman a upward means alternate means not adjacent sorry for that word not adjacent alternate ok so alternate means interior because all the four angles are in interior so as you see the drawing interior angle word here as soon as word interior is said so just see the inner angles now in this alternate Which are the alternate? Alternate means One is here, so its alternate will be here The zigzag formation So the zigzag formation happening here This one This is zigzag formation Means after this angle I am talking about this angle So, this will be called alternate interior angle. Similarly, angle 5 is alternate interior. angle to angle 4. So, this is a pair of angle 5 and angle 4. Angle 4 and angle 5. These are alternate interior angles.

Is it clear, kids? Next, what is a pair of alternate exterior angles a bit of a day interior album putting an exterior or exterior may happen to get char angle they watch our angle kakao they watch our angle your exterior metha yeah and the one yeah and the two yeah and the seven yeah and the late yeah exterior angles a bargain goes a it's my alternate exterior comes a hammer term a one key bath Karu the one came on next exterior angle just opposite may have alternate may have So, here you can see that the pair is angle 1 and angle 8. Angle 1 and angle 8. Is it clear? Similarly, if I talk about angle 7 and angle 2. So, angle 7 and angle 2 are alternate exterior angles.

So, when you have to say alternate interior and when you have to say alternate exterior. This thing should be known in this chapter. Last thing I would like to tell you is pairs of interior angles on the same side. side of the transversal.

Means, understand this thing also. That this is the transversal. On the one side of this transversal, means if I talk about this side only, then these interior angles, these two interior angles, the sum of these two is 180 degree.

These are supplement angles. Now, this is the transversal. Now, This is the interior angle of the transverse cell. So, the sum of angle 5 and angle 3 is 180 degrees.

So, you should know the word which are the two pairs which are in interior. Which are the two pairs which are in interior are angle 3 and angle 5. Angle 3 and angle 5 are on the same side. Okay? pairs of interior angles on the same side of the transversal.

Transversal ke same side pe interior angle hai. Angle 3 and angle 5, angle 4 and angle 6. Ab ye naam Through this chart, you have learnt some names And you have understood to see the drawing When two lines are given and transversal is given So what are the names of angles Who will be called interior Who will be called exterior Who will be called alternate interior Who will be called alternate exterior Who will be called corresponding And which one will be called on same side same side of a transversal interior angles you understood these words now what are the relation between them we will see in our next slide because transversal is very important so it is important to understand is it clear next understand the main point here three points what are these three points First point, if two parallel lines are cut by a transversal, if two parallel lines are cut by a transversal, if two parallel lines are cut by a transversal, then each pair of alternate interior angles, then each pair of alternate interior angles, alternate interior angles, now which are these? Understand this is interior, then its alternate will be, so, Alternate interior angle are equal.

When this line is parallel, the drawing which is made in front, there are no parallel lines in this drawing. So, most of the kids say angle 3 is equal to angle 6. There are no parallel lines. Keep this in mind. That's why this drawing is kept here.

This is not equal to angle 3. Angle 3 is not equal to angle 6. This is a condition when there are two parallel lines. Note this point. I am making a drawing here. Try to understand this. If two parallel lines are cut by a transversal, through a transversal, then we will call this line as transversal line.

Each pair of alternate interior angles are equal. These are alternate interior angles. So if this is angle 1 and this is angle 2, then I will say angle 1 is equal to angle 2. Clear?

Second thing, here they said if two parallel lines are getting cut from a transversal then each pair of interior angles on the same side of the transversal are supplementary. Now I have told you that if anyone cuts two parallel lines from a transversal So, on one side, the sum of the interior angles will be 180 degree. If this angle is 3 and this is angle 5, then the sum of angle 3 plus angle 5 will be 180 degree.

Remember this because it will be very useful while solving the questions. Clear? Let's understand one last point which I think is important to give you guys.

If two parallel lines are cut by a line, see these are two parallel lines. If two parallel lines are cut by a line, then this line is called transversal line. Each pair of corresponding angles means this angle. and this corresponding angle I have explained it in the back so this angle is corresponding to this angle it will always be equal these are called equal angles in parallel case so angle 1 is equal to angle 5 angle 1 is equal to angle 5 parallel lines now this line is not parallel but understand if here angle 1 is and angle 5 is then what? if this is angle 1 and this is angle 5 then angle 1 is equal to angle 5 in parallel line condition clear kids?

same way corresponding angle is if I say here angle 3 is then angle 3 is corresponding to angle 7 then these two will be equal in parallel line angle When? When two lines are parallel, it will have a transversal cut. So you note this point, corresponding angles are equal in the case of parallel lines. So children, you have learned a lot of words so far.

Its first chapter is, find the complement. Look at the word, please catch the word. I have taught one word in theory, what is supplement and I have taught one word in complement. So find the complement of each of the two. of the falling angle.

Compliment, the first thing I taught was compliment. Compliment means the sum of two angles should be 90 degrees. Now pay attention here, if one angle is given to you of 20 degrees, then what will be its compliment angle? If I have given a 20 degree angle and I say that I don't know its compliment, this will be, I say X, any value.

We have solved the simple linear equations. So, I will form an equation and do it. 20 degree plus x.

And I know that word complement means the sum of two angles will be 90 degree. It is clear. So, So, from here you see the value of x and the value of x is 90 minus 20 that means 70 degree. So, what is the complement of 20 degree?

The complement of 20 degree is the angle of 70 degree. Means what you have been told here is that the angle given to you is only of 20 degree. If I want to make it a complement, means to form the angle of 90 degree, then I have to make it 70 degree. degree or add karna padega 70 degree so that means the complement of 20 degree is what 70 degree ye hai iska solution aage dhyan dena ab ek angle mujhe iss form me diya hai theek hai sir yaha pe toh kuch hume samajhi nahi aara hai ye angle hi ulta diya hai aise niche bana hua hai 60 degree ka angle hai iss me hum kya kare deko tumhe kuch nahi karna tumhe abhi piche chapter padha hai chapter number 4 simple equation yaha pe equation formation karlo deko. So, I have given one angle 60 degree and if I ask its complement, then I add x degree in it.

I don't know what that angle is, I have to find out the complement. So, if I have added x in 60 degree, then the sum of these two should be 90 and complement. This is the meaning of 90 degrees. So how will you get the value of x?

This will be 90 minus 63. And how much is 90 minus 63? 3 out of 10 is 7 and 6 out of 8 is 2. That means 27 degrees. I have to add another angle of 23 degrees before 63 degrees.

This angle will be of 23 degrees. And the sum of both will be 90 degree. So this is your complement.

Is it clear, kids? Okay. Now pay attention. There is a third part of this.

Again, you have given 57 degree. And if you have asked for a complement of 57 degree, then this will be the sum of these two. 90 and what will be the value of x?

This will be 90 minus 57. How much is 90 minus 57? 7 out of 10 is 3 and 5 out of 8 is 3. So, here you will get 43 degrees. So, 33 degrees is the complement of 57 degrees.

So, this was the first question. Let's see the next question in which word supplement is used. Question no.2 in NCIT book is, you will see in this it is said find the supplement of each of the falling angles what angle is given 105 degree and according to the supplement we know when I add x in 105 because I don't know this angle we have to find out supplement angle ok so what should I add in 105 that the sum of two angles is 180 degree this is the meaning of supplement so this means what will be the value of x x will be 180 minus 105 and 180 minus 105 means 5 on unit place and 7 here and 75 here so this is your answer if I add 75 more in 105 then here our x is 75 and 75 is 75 so this is your answer angle aega matlab dono ka sum aega 180 degree.

To supplementary angles supplement the supplement of 105 is 75 degree. Aise hi the supplement of 87 degree the supplement of 87 degree kitna hoga. The supplement of 87 means 87 plus x is equals to 180 degree or yaha se x ki value ki aegi ye aegi 180 minus 87. and you will see that 7 out of 10 is 3 and 8 out of 17 is 93 so 93 degree is the supplement of 87 So, you can get to see some good questions like this in 1 or 2 marks in the exam.

You guys tell me the answer to this. What will be the supplement of 154 degree? So, what should I add in 154 degree that my...

sum 180 is equal to 180 minus 154. And 180 minus 154 is 6. And 5 out of 7 is 2. So it is 26 degrees. So when I add 26 to 154, then 180 will be... Simple equations. which we have read in the previous chapter similarly you have to do equation formation and solve it here is it clear kids no one has any problem let's see the next question next question is identify which of the following pairs of angles are complementary and which are supplementary here you should know that complementary means sum of two things 90 degree and supplementary means sum of two things 180 degree now you find the pair here see here it is 65 degree so 65 degree and 150 degree if I add these two see 65 plus 115 so how much came see 5 5 10 came 0 carry 1 7 and 8 and here 1 so you will see 65 plus 115 and 180 is coming, it means this is a supplementary pair, it is clear, if you do 63 plus 27, then you will see that 90 will come here and what does 90 mean?

This is a complementary pair. So, we write C here. You have to add it like this. Tell me, if you add 68 in 112, as soon as you add 68 in 112, then it will be 180. This means that this is a supplementary pair.

So, I am not showing you by solving it. I am just telling you to add it. And tell me, if we do 130 plus 50, then what is 130 plus 50?

180. Now, what does 180 mean? 180 means this is a supplementary pair. Supplementary means both should have sum of 180. 45 plus 45 what?

181. And 90 means, what is this angle? It is a complementary angle. So you should know the pair. This pair is supplementary and complementary. Now 80 plus 10 means 90 degree.

So 80 plus 90 is 90. 90 means this pair is complementary. So this was question number 3. Let's see the next question. Next question is, Find the angle which is equal to its compliment Joe up any compliment came about a burrow of a single compliment come at the author 90 degree so as a angle but oh Joe up any compliment came about a burrow matlab do no equal who need a the 90 k I got my dope art cardoon So, 45 degree, you will get to see that 45 degree. So, I will say that angle is 45 degree. If I say that the angle 45 degree, which is equal to its complement.

So, what will be the complement of 45 degree? that too will be 45 degree 45 degree's complement will be 45 degree so 45 is equal to 45 both angles are equal means the angle is equal to the complement this is what I asked in this question Similarly, you can get a question in two marks in the exam. It is important that tell two angles which are equal to each other and equal to their supplement. So, the supplement angle means 180 degrees. The sum of two angles should be 180 degrees.

And when I divide 180 into two parts, what will happen? Half of 180 means 90 and 90. If I take angle 90 degrees, then what is the supplement of 90 degrees? 90 degree supplement is 90 degree. It is clear, kids. See, 90 degree supplement is 90 degree.

So, find the angle which is equal to its supplement. It is here. It means that 90 degree angle is talking about which is equal to its supplement. Such questions come in 2 marks and 1 mark in exam.

Pay attention further. Next question is, we have given you a figure. The angle 1 and angle 2 in this figure are supplementary angles of each other.

This angle and this angle have a sum of 180 degrees. So, this is a straight line. So, you had studied a linear pair in theory. And you had also told the meaning of supplementary.

Supplementary means 180 degrees. In linear pair, two angles which are adjacent form supplementary angles. Angle 1 is supplement to angle 2 and angle 2 is supplement to angle 3. to a supplement to angle one. Now what is said ahead, let's read that. If angle one is decreased, decreased means less.

Now see this very big obtuse angle is visible. Obtuse means big angle is visible. Big angle is visible. It is a very big angle.

If I start decreasing this big angle, okay, he is saying this. What changes should take place in angle two? What changes will you see in angle two? Now as you start decreasing it, will start increasing because the common arm will start the movement. Suppose I take this straight line and I reduce angle 1. So angle 1 which was looking very thick now it looks very thin, it was looking obtuse and it looks acute.

But you will see here that angle 2 which was acute, it became obtuse. So this is what I am asking you that what changes are you seeing? we will get to see that if we decrease angle 1 then angle 2 will increase that both the angles still remain supplementary If both the conditions are supplementary, then if I decrease angle 1, then angle 2 will increase.

A simple statement will come that the changes that take place when angle 1 is decreased is that angle 2 measurement will increase. The measurement of angle 2 will start increasing. Only this question can come in two marks.

Next question. Let's look at question number 7. Can two angles be supplementary if they are acute? Please try to understand what I mean by acute. Acute means 90 degrees smaller than the angle.

90 degree say Chota 90 degree say Chota may is come on let on 80 degree go take it or supplementary come at love kia hota supplementary come at love do angle custom in the angle custom 180 degree on a chee you supplementary come at love to you you know I'm gonna angle acute a acute one of the 90 degrees a chotey hey take a malayalee 80 here or is ko ma at max 89 lay sat down 90 to lay in a sector koki acute will a 90 B Nio 90 second moon achieve the 89 degree be later in the no custom cabin 80 are I So you will see that the sum of both these angles is not 180. So always remember that two acute angles will never form a supplementary angle. I have solved a question in the back. In that question, the supplementary angle means that the sum of both the angles is 180 degrees. And if you take 90 degrees at max, Acute angle is always less than 90 degrees So the supplement of the second angle will also be 90 degrees So always remember Now before this we have seen a condition in the question As I will reduce one angle, the second angle will increase So both are acute, this condition is not possible Both are obtuse, this condition is not possible Acute means smaller than 90 Obtuse means bigger than 90 Remember this way, some kids don't remember obtuse and acute.

The initial word of obtuse is O. O means round and round means thick. Thick means bigger than 90. So, remember something like this.

There are many ways to remember. Obtuse means the word fat. Now fat means what?

That is, bigger than 90. Fat means bigger than 90. So, two bigger than 90. If I take one bigger than 90, then the other will be less than 90. So, two obtuse angles will never do supplementary formation. Second thing, both right angles. So, you can see both right angles 90 and 90. This supplementary formation, formation kar sakte hai toh can two angles be supplementary both of them are right question mark yes iss case mein aayega yes aur in dono case mein aayega no and no clear hai bachcho toh yaha tak humne question number 7th dekha exercise 5.1 ke andar ek hum aage aur dekhte hai question question number 8th bhi dekh lete hai iss exercise ka wo kya hai an angle is greater than 45 degree ek angle hai 45 degree say but I have is its complementary angle was conjo complementary angle Hoga greater than 45 degree yeah whoa 45 degree say but I'll go word complementary come at last sir apne batata two angle sum is 90 degree.

Now understand the thing. If there is one angle of 45 degree, then if I assume its complement is x, then what should be the sum of both of them? The sum of both of them should be 90 degree according to complementary. So, I am seeing the value of x as 45 degree only. 90 minus 45 will give you 45. What question have you asked?

Angle is greater than 45 degree. Is its complementary angle greater than 45 degree or equal to 45 45 degree. So you will see that its complementary angle is equal to 45 degree. Neither less than is coming nor greater than is coming.

Okay. It is coming equal to. So word equal to is your answer. This was question number 8. You can get such questions of 1 1 marks in front of you.

See the next question. He is saying that you have given a figure. You are seeing a figure behind me. He is saying that you have given a figure. Inside this figure.

angle 1 You have to tell us, the question mark is given, is angle 1 adjacent to angle 2? Is angle 1 adjacent to angle 2? What does adjacent mean?

Adjacent means adjacent. So is angle 1 adjacent to angle 2? Yes, Abhishek sir, you told that you have to check the adjacent angle. So there should be a common arm. So sir, there is a common arm between these two angles.

That means these two angles are adjacent to each other. Yes. answer is yes.

Second is angle AOC adjacent to angle AOE? both have O and O that means angle formation is happening on point O this is point O now what they have given is AOC so pay attention A O and C is here so they have talked about this angle angle AOC this is angle 1 they have said that is this angle adjacent to angle AOE angle AOE This is the whole angle. So, you will see that the angle next to it is called adjacent.

But here the angle AOC is coming inside the angle AOE. It is not in the adjacent. It is covering it. It is not in the adjacent. So, in this case, because he asked us a question, we will say no.

Clear? After that what did they do? Do angle COE I will correct it a little Now see the drawing What is said?

Do angle COE This angle COE And angle EOD EOD This is the whole big angle Now, he has said do angle COE and angle EOD form a linear pair? These two angles, angle 2 and angle 3 plus angle 4. So, this is the question. Are these angles forming a linear pair?

A linear pair is a combination of a common straight line and a supplement. If the sum of these two is 180 degrees, then the angle of the So, we will do this because we can see a straight line here. These three angles are on a straight line. Okay, if we talk about two angles, then angle EOC and angle EOD are on a common line. So, we will say yes, a linear pair is being formed here.

Next, R angle BOD, I will correct it. Please note that we have talked about angle BOD Where is BOD? Here it is We are talking about angle 4 What?

And angle DOA DOA is angle 5 ki baat kar rahe hai. Thike hai? Supplementary. Kya yeh dono angle supplementary hai? Haan.

Agar line common hai in dono angle ke beech mein A, B line common hai, straight line hai, toh hum kahenge angle 4 plus angle 5. 180 degree here that means here linear pair is being made we will say this is supplementary angle yes what is said further is angle 1 vertically opposite what is he saying I am asking you angle 1 is here angle 1 angle 1 is vertically opposite of angle 4 yes vertically opposite means sir you told me what is the vertically opposite angle of angle 5 what is the vertically opposite of angle 5 yes Check this angle. This line is gone and which line is cutting? This line is cutting.

Now what is the vertical opposite of this whole angle? What is the vertical opposite of angle 5? So you will see this whole angle means angle 2 plus angle 3. This is its Vertically Opposite Angle and Angle 2 plus Angle 3 means What can I say?

COB This is your Angle, Angle COB This is our answer So, you understood this question. It was a very good question. You can see this drawing, it is also given in NCIT.

And these are some questions. In True and False or in Filling in the Banks, you can ask these questions from this chapter. Half of marks, one mark can form many questions. This chapter is a very good chapter to gain small marks. Next question number 10th is Indicate which pairs of angles are vertically opposite angles You tell me, I have a drawing in front of you Which angle is vertically opposite to each other Come on, pay attention Which two lines are intersecting each other completely So I will say this line And this line is cutting each other So see, first we will hold this line And hold this line Now, where all the vertical opposite angles are to be formed.

Please note that this is angle 5. Its vertical opposite is this whole angle. So, we will say angle 5 is equal to angle 2 means we have to tell the pairs of vertically opposite angles okay so we will say angle 5 comma angle 2 plus angle 3 these two are vertically opposite angles these are pairs of these two sum similarly angle 1 and angle 4 are vertically opposite angles this angle 1 and this angle 2 angle 4. Clear hai bachcho? To ye the aapke Vertically Opposite Angles. Fir wo tumse puchh hai linear pair kahan kahan ban rahe hai. Chalo ish drawing ko thoda clear kar lete hai.

Linear are those pairs which form 180 degree on straight line. So, this straight line is visible. What can I say on this straight line? Angle 1 and angle 5. These are linear pairs. Angle 1 and angle 5 because these are on straight line.

Then, you can see a straight line here. On this straight line, we will say angle 4 and angle 5. These are linear pairs. Clear hai bachcho. To angle 4 and angle 5 ho gaya.

Angle 1 and angle 5 ho gaya. Aur kon kon se angles hai jo linear pair formation kar rahe hai. To ye hai angle 4. Angle 4. Aur angle 3 plus angle 2. These are also linear pairs. I have already told you about pairs. What is a pair?

Angle 4 and angle 3 plus angle 2 the combination of these two and angle 4 is also a linear pair. So, you can give it like this. And you can see here angle 1 angle 1 if I hold this straight line, angle 1 and angle 2 plus angle 3 So, angle 2 plus angle 3. These are also linear formations. You should know from the figure that what are the vertically opposite angles and where are the linear pairs. So, you can get to see this question in 2 marks in the exam.

There is one more question. This is also a good question. See. In the following figure, angle 1 adjacent to angle 2 is.

The word is put ahead. Is. What? What?

He is asking a question. Is angle 1 adjacent to angle 2? Give reason. Sir, you had told that the adjacent should be a common arm.

Pay attention. Here, one angle is 1 and another angle is 2. So, is this a common arm, sir? Okay. It is.

Then, you had said that the two non-common arms should be on either side. Sir, these are also on either side. I had said it immediately. So, is this angle here?

angle 1, I will say in the adjacent of angle 2, not in adjacent, these are opposite angles, opposite interior angles I had told you because this line is parallel to this line, we can see and here a transversal is being cut, so here it is not adjacent, we call it opposite interior angles. Opposite sorry alternate opposite angles. Okay.

These are opposite alternate angles. We had read it at the back. So opposite alternate angles.

Means after 1, angle 2 is being formed on the other side. For adjacent, we had read that if this line is there. Okay.

And this line is there. So here common should be on one side. On the other side, it should not go separately.

Either side means on the one side of this common arm. Both. non-common sites should be there.

So, these will be adjacent angles but these are not adjacent. We have read the word behind this. When you will visit theory in the theory video, we have read the name for it.

Is it clear, children? Come on, pay attention. Next question is, find the values of the angle x, y and z. He is saying that you have two figures. In this, tell the value of x, y, z by looking at the figure.

Now, pay attention. Sir, when you were teaching theory, you said that vertically opposite angles are equal. y is equal to z and 55's vertically opposite angle is x.

Because these two lines are intersecting lines. This vertex is intersecting. This is intersecting vertex.

So, So, we can see the value of x is 55 degrees. If you are able to tell x, then you had told that on a common line, this is the common line that we can see, on this common line, this angle x and angle z, both of them are supplementary angles, meaning they are forming a linear pair. So, can I say that angle x is 55 degrees, plus angle Z which is 180 degree. You can say it right away.

And you have found 55 above angle X. So if 55 is there, then what will be the value of angle Z? Very good.

Tell me quickly. 180 minus 55. So 180. minus if you do 55 then what is your value coming out of 10 5 5 and 7 out of 5 here children 2 125 degree so sir we have taken out this angle z this is coming 125 degree if you understand this much then after angle z you will be able to take out angle y because it is a vertically opposite angle so this will also come 125 degree Clear? The question is of 1 and 2 marks.

You can see it in the exam. Next, this figure. This figure is also good. There is a straight line here. There are 3 angles on one side.

This, this and this. The sum of these 3 angles. Angle 25. The 25 degree angle.

25 degree. plus 40 degree by a angle plus a angle or plus x degree. This linear pair formation means it will be 180 degree.

Now 25 plus 40. 25 plus 40. Solve it quickly and tell me what will be x. So 25 plus 40, your answer must have come. How much did it come here?

It came 65. 65 plus x is equal to 180. And sir, we have taken out the value of x. Tell me what is the value of x? The value of x is 180. You do minus 65. So let's go.

What is the value of x here? 5 out of 10 is 5. And 6 out of 7 is 1. 115 degrees. So what is the value of x here?

So, you will see that it is 115 degree. So, the value of x is obtained. Now, after this, can I say that, see carefully in the figure, I will rub it. If this is 115, So, two lines are visible while cutting. One is this line and the other is this line.

Can you see? Sir, is this 40 degree vertical opposite angle? Yes, it is.

So, it means that the value of z is also 40 degree. If z is 40 degree and x is 115 degree, then what is left? y.

You can calculate y. See, two angles are forming on this line. angle z and angle y.

So, can I say angle z plus angle y is a linear pair and supplementary angles are always supplemented. It means the sum of these two is 180 degree. Sir, you had taken out 40 from angle z.

So, we will take out the value of angle y. So, very good. If you are getting this idea, then take it out quickly.

How much is the value of angle y? Very good. 140. So, you saw that angle y is very good.

So, you can see that angle y is value 140 degree is given. These type of questions are more preferred by teachers. These type of questions are given in 3 marks and 2 marks.

To check whether you know the names of angles, you know to calculate angles or not. So this question can come there. We will see one last question in this. Question number 13th is also there.

It is a question of filling in the blanks. This question is asked in many exams. You tell me if you have FULLY If you have seen our theory video then you will give the answer quickly. What is the first line?

If two angles are complementary, If two angles are complementary, If the word complementary comes, 90 degree figure should be visible in your mind. This 90 degree should be visible quickly. Did you see? If two angles are complementary, Then the sum of their measure, Quickly, 90 degree, This is what came in our mind while listening to the word complementary.

If two angles are supplementary, Then the sum of their measure, Sir, as soon as we heard the word supplementary and we have seen your video, then our answer came quickly 180 degree. Okay. Two angles forming a linear pair. There are two angles forming a linear pair.

What will be R? They will be supplement. Are supplement to each other. Are supplementary angles. Clear hai bachcho?

To supplementary yahaan pe word likhte na. Aage, if two adjacent angles, agal bagal me lage hue jo angles hote hain, if two adjacent angles are supplementary, they form a, wo kya form karenge? Ab do adjacent angle agal bagal lage hain, aur wo 180 degree formation kar rahe hain, to wo linear pair form karte hain. Ye hamne theory me pada tha. Clear hai bachcho?

Chal ye. Isme aur, Let's see those flinging the blanks. What are those flinging the blanks?

If two lines intersect at a point, then the vertically opposite angles are always equal. We have studied this theory. Is it clear?

Both vertical angles will be equal to each other. If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, if one pair, means if these two pairs are acute and 90s are small, then we make it smaller. See, this is a pair and this is a pair of acute angles.

If one pair is of acute angles, then the other pair is of obtuse angles. Always remember this. So, they asked the same thing, if two lines intersect at a point, if one pair of the vertically opposite angles are acute angles, then the other pair of the vertically opposite angles are what?

If these are small, then these will be big. Obtuse, acute, obtuse are obtuse. Angles.

Clear hai bachchu? So, these are the easy questions that are asked here and you should know. There is one more question in front of us.

14th question is also in NCERT. What is that? In the adjoining figure, you are given a figure again named the following pairs of angles. If you have understood that whole chart well in my theory lecture, then you will understand it easily.

In this, it is asked which are the obtuse vertically opposite angles? Thick and vertically opposite angles. We have read in the last question. Okay, see here, we can see a figure.

There are two lines intersecting each other. This line intersecting this line. Okay.

Here, this acute is visible. Okay. Now, which is obtuse? This whole and this whole.

So, we will call angle Bod. Okay. We have to tell the pairs of obtuse, vertical and opposite angles. So, Bod. Okay.

And BOC. Angle B O C What is this? This is obtuse vertically opposite angle After that Adjacent complementary angles Complementary angles in the front and back Means the 90 degree formation That we are doing Pay attention here I will clear the board and I am looking at the second part of it. Adjacent means 90 degree of complementary. Complementary angles.

So, you understand the thing that complementary means 90 degree. Now, while making 90 degree, which angle is visible here? We can see that in the adjacent and complementary angle. Now if you see here, you can see A, O, B, this is one angle and its complement angle is A, O, E.

angle Bod is complement to the angle EOA. Bod, EOA. Here 90 degree formation is happening by combining both angles.

So, this complementary word was given to us. I have told you the adjacent complementary angle. This pair is understood. Here is that pair.

Ok. Next, what they have asked? Equal supplementary angles.

What is equal supplementary angles? Supplementary angles means such angles which are forming 180 degree. Now, they have said that which are the equal supplementary angles you can see here. So, what are the equal supplementary angles I can see? See.

Equal. angle DOE angle DOE is equals to angle BOE this one and this one. So here will be angle BOE This is equal b and the supplementary b of one another means they are making 180 degree by joining together they are on similar line In that they asked unequal supplementary angles Which are unequal supplementary angles? So you see here BOC angle See BOC angle This angle BOC is a supplement of angle DOC and these are unequal so I am adding not equal to but why is this pair? No You understood this.

I have written an answer of equal supplementary here and an answer of unequal supplementary here. So, these are the three answers in front of you. Last is adjacent angles. Angles in the front and back.

Do not form a linear pair. Those who are not forming a linear pair, means not on a similar line. But they are in front and back.

There will be many angles. See this. I can see one or two.

See. DOE. Where should I write?

I will write here. Angle DOE is adjacent to angle EOA. Is it clear? Are you able to understand? Both the angles are adjacent to each other.

Then you can say angle EOD. angle EOD is adjacent to COD so here angle COD will be given is it clear? so angle COD is also given this is the adjacent angle here I have written so form such angles tell me here which will tell in the comment box tell that which are the other angles that you are seeing here that adjacent angles are not forming a linear pair.

So, till here we have NCRT 5.1 question number 1 see you have been given a figure in it and by showing the figure you have shown angles and a simple statement is written and that is state the property property ka naam batana hai. To humne 5.1 me kuch properties dekhi thi aur theory part me bhi kuch properties dekhi. Wohi properties ko aapko yahan batana hai. Jab mai koi statement bol raha hu to ye mai kyun bol raha hu. Uska reason kya hai.

To aapko wo reason dena hai. Property likhni hai iske saamne poora statement. That it is used in each of the following statement.

Matlab ye jo humne statement bolay hai, tino. Ye hum kyun bol rahe hai. Ye bolay hai, ye sahi hai. But why did he say this? What is the reason behind this?

So whoever has attended the Theory lecture very well, whoever has watched that video, they will give the statement of this in a short answer. Pay attention, listen carefully. What is the first statement? He is saying, A line. A parallel is of B.

So, if you see the figure then A parallel is of B. Can you see? A parallel is of B. Why is it said in the question?

Because it is said in the first statement. If A parallel is of B then comma then angle 1 is equals to angle 5 that means angle 1 is equals to angle 5 and when we read the properties then we understood that this angle is being made and this angle is being made and this angle is being made this is cutting a transversal to parallel line so these two angles are equal why they are equal? which angle is it?

angle 1 and angle 5 are which angles? these are called corresponding angles When a transversal cuts the parallel line, here you will write, give a reason because they have asked for property. So, these are corresponding angles and corresponding angles are always equal.

We know that corresponding angles are equal when transversal, when the transversal cuts the parallel lines. When a transversal cuts a parallel line, corresponding angles are equal. That means angle 1 is equal to angle 5. So, what you have to do is, you have to write a statement.

You have to identify those angles, and which property you are using. So, these parallel lines, because corresponding angles are equal, so these corresponding angles are equal. Read the second statement. In the second statement, it is written that angle 4 is equal to angle 6. What is it saying?

Angle 4, we will clear it and see. It is saying that angle 4 is equal to angle 6. Now understand the thing, where did one angle come? Zigzag form.

formation vana hai yaha pe zigzag formation mein baat ko sabah na angle 4 equals to angle 6 alternate interior angles are equal when the when the transversal curves parallel lines theek hai toh kaunsa angle hai yeh kaunsa zigzag formation ke andar maine theory mein bataya tha zigzag formation ke andar aapka alternate interior angles yeh dono interior angle angle 4 be interior angle 6 be interior but alternate mein hai. To alternate interior angles are equal. So angle 4 equals to angle 6 then A is parallel to B.

Ye statement bolay hai. Agar zigzag formation mein angle 4 angle 6 ke equal hai to iska matlab A parallel to this line. This line is parallel to this line. This is the property.

You just have to tell that alternate interior angles are equal. Here we will write the statement alternate interior angles alternate interior angles are equal Alternate interior angles are equal when transversal cuts parallel lines. Clear hai bachcho?

So, this was your second point. You have to write this statement. This is what they said.

State the property. Which property did we use? We used the property of alternate interior angles.

Okay. After that. If angle 4 plus angle 5. He is saying.

If I see angle 4 and angle 5. See angle 4 and angle 5. This angle and this angle. Okay. If I plus this angle and this angle.

So, 1. 180 degree my sum will come. At this time A will be parallel to B. So this statement is said. Yes, when did you say this?

If you have attended theory lecture then I had told you that the interior angles are what we will write in statement? We will write in statement interior angles on the same side of transversal. These are interior angles and on the same side of transversal. So, here what property you will say, which we have read, watch the video, I have read all this. Interior angles on the same side of transversal.

are equal clear hai bachchu toh aapko kya karna hai is question mein jaya tar bache confused hote ho 1 marks 2 marks mein question aata hai exam mein teacher jo bhe aapko question dena chahti hai wo chahti hai iss chapter ke andar ki aap figure dekho aur cheech ko dhund pao ki bhai Which property is being used? Is it clear? So we have to use the property and we have to state the property. So these three things I have told you how to write here. You have to give the answer in a simple statement.

Is it clear? Clear? Here are interior angles, alternate interior angles, and these are interior angles on the same side. And here corresponding angles are equal. Clear?

Let's see the next question. What is in the next question? Look at question number 2. Again it is saying in the adjoining figure. Adjoining figure means the figure next to it.

The figure next to the question we have written. Here we will give you the number of that figure. Here it is written in the adjoining figure.

The figure given to you next to it. Identify. identify what identify means find what find see the pairs of corresponding angles tell all those pairs which are making corresponding angles ok now understand the thing corresponding angles only then you will be able to tell when some parallel lines or some two lines are being cut transversal so here we can see C is transversal If this is a transversal, means if it is a transversal, that someone is cutting two lines A and B with C.

Now in this I have to tell, pair of corresponding angles. So what are corresponding angles? Transversal, one angle is forming here, This is the same angle formation here. So, we will say angle 4. We will say the pair. So, we will say angle 4, angle 8. This is one pair.

Clear? So, the pairs of corresponding angles. We have told this.

Then, what are the corresponding angles? Angle 3, angle 7. See this. Angle 3 and angle 7. See, they are looking the same.

The angle is being cut by the angle and the angle is being cut by the angle. That is why we call it corresponding angles. Okay.

Similarly, if you see here it is 5 and here it is 1 then we will say angle 1 angle 5 similarly if you see here it is angle 2 and below side formation or angle 6 a key side pay the angle to comma angle 6 yeah have pairs corresponding angles key clear hey so yet our first part case a attempt gonna pay us with an ATA I'm a pair's but are the a was given second part we can push a pairs of alternate interior angles alternate interior angles interior model under ganglito sub-sabha la panna Zara question pay Jesse a question they hug a topical interior angles they can a interior angles can again angle three angle Angle 2, Angle 8, Angle 5 are interior angles. But don't give answers in haste. We have asked in question, Alternate. I had told you about Alternate. That one thing is here, so the other thing will be on this side.

Means in zigzag formation, we tell alternate interior angles. So see here, a zigzag formation is happening. In this zigzag formation, if you see carefully, then 3 is interior and 5 is interior. So, what will be the pair?

Here, the pair will be angle 3, angle 5. Angle 3, angle 5. These are alternate interior angles, kids. Similarly, you will see that in this zigzag formation, one formation is happening here also. This is also a zigzag formation. In this zigzag formation, interior angle is angle 2 and angle 8. So, we will say angle 2, angle 8. So, these are alternate interior angles. This is our second part.

After that, what is said? Tell the pair of interior angles on the same side of the transversal. Which is on the same side of the transversal.

So, you see where is the transversal? This C is the transversal. And one side of the transversal is this and one side is this.

Okay. Now, what are the interior angles on this side? So, tell me the interior angle on this side is angle 3. this is a pair and always remember that the sum of angle 3 plus angle 8 is 180 degree if both are parallel lines if both are parallel lines and transversal is cutting it then interior angles on the same side of the transversal are their sum is 180 degree ok not equal but sum is 180 degree so here 3 and 8 and here 2 and 5 so here 2 and angle 5 so these are the angles interior angles on the same side of transversal this side 3 and 8 and that side 2 and 5 I asked interior angles interior means inside the vertically opposite angles now which are the vertically opposite angles if you see the vertically opposite angle then vertically opposite means I told you in the video where ever there are two intersection points sorry where ever there are intersection points and I insert the So, the cutting intersection point is the one with the vertically opposite angle. I have told you this in theory.

This means that if you see here, a transversal line is being cut. So, I will say angle 4 is the vertically opposite angle of angle 2. So, we have to tell the vertically opposite angles. So, we have to tell the vertically opposite angles. opposite angles, I will write it here, pay attention, this is angle 4, angle 2, vertically opposite angle, angle 3, angle 1, angle 3, angle 1, vertically opposite angle, similarly angle 8, angle 6, angle 8, angle 6, vertically opposite angles, similarly angle 7, angle 5, so angle 7, angle 5, this is vertically opposite angles, so you are understanding the angle. It is very easy.

You can get such questions in the exam. Let's see our next question. What is he asking us in the next question? In the next question, he is asking us.

What is in this question? In this question, you have a figure. Now in this figure, you are clearly told that P is parallel to Q.

P is a line which is parallel to Q. And you are told that at an unknown angle, find the unknown angles. So, you can see the unknown angles there. What are the unknown angles? So, how to attempt this question?

To attempt this question, first you have to write the solution. Then you have to write given. Now, understand that given is the given me kya hai? Tumhe given me yaha pe P parallel diya hai Q ke.

Thike uske baad tumhe bola hai to find. Pata karna hai. Kya pata karna hai bhai?

Hame pata karna hai angle A, angle B, angle C, angle D, angle E and angle F. Total 6 cheeje hame yaha pe pata karna hai. 6. and we have to find the alphabets and for reference we have given an angle if you see carefully this is the angle 125 degree this is given for reference and if this line is parallel to P and Q as it is said in the question then this means this line I will call this as transversal because if these two are parallel lines then this line is cutting them we can see this in the figure so what I will write here pay attention, I will write here as we know what do we know?

what do we know? we know that 125 degree 125 degree plus angle F Yes, some 180 degree huga Sir, guess a but I'm it guess a but I'm a but I know I got up with your electric video. Thank you So skin the minute you some Jai Kiko straight line pay a girl going to angle has straight line pay a girl co e do angles a girl bugger matlab adjacent to each other hey don't don't know about some 180 degree hotel in your pair concept yet canna using linear pair here pelican a teacher Kobe I'm a butana Zara really hey Kim an AET each kill lucky hey the using linear pair concept yeah property using linear pair property Nikki happy clear Linear pair I have explained to you. 125 degree plus F. So, from here you can calculate angle F.

And angle F will be 180 minus 125. And when 125 goes out of 180, then 5 out of 10 goes here. And if 2 out of 7 goes, then again 5 goes here. So, this is your 55 degree angle F.

You saw that I have one thing today. and this is angle F this is 55 degree so can I say that angle F is equal to angle E why sir why are you saying that angle F is equal to angle E pay attention here there is an intersection of things this intersection at this point is called vertical opposite angles are equal to Vertically opposite angles are equal So here we will write What? First of all we will write here What? By making an arrow in front of it That vertically opposite angles are equal Vertically opposite angles are equal This means I have calculated angle E. No one will have any problem here.

We have calculated F and E. Now what is the task in front of us? Pay attention, now what is the task in front of us?

A, B, C, D calculate. Remember, here properties will be applied which are the angles of parallel lines. See, these are parallel lines which are cutting transversal. So, can I say that on the same side of transversal, interior two angles angle F and angle D both of them will have sum of 180 degree.

Again, here we will write as we know, what do we know? We know that angles on same side of transversal, which angles? Interior angles.

So, please mention here. I am writing interior here. Please remember, as we know interior angles on the same side of transversal are supplementary. So, I have written SUPL, supplementary. So, this means angle F and angle D.

Angle F plus angle D, their sum will be 180 degree. And angle F, you have calculated. Angle F, how much?

angle F is 55 degree. So, if angle F is 55 degree, then what will be angle D? Tell me in the comment box.

If everyone has copied, then I can see some space here. I will do it here. Remember angle F is 55 degree.

angle D will be 180 minus 55. And what does 180 minus 55 mean? 180 minus 155 means 5 out of 10 is 5 and 2 out of 7 is 5 and 1 is 125 degree. This means angle D is also calculated and this is 125 degree. Is it clear? Now, remember angle D will be equal to angle B.

Vertically opposite angle, here we can see a cross section, an intersection point and here we can see vertically opposite angles so vertically opposite angles are equal This is 125 degree, so angle B will also be 125 degree It is clear Now, understand the thing that if these two parallel lines are cutting transversal then corresponding angles are equal This angle, corresponding angle corresponding angle. Both are on the top side. E and A.

So, whatever value of E comes, E's value is 55 degree. So, this means that A will also be 55 degree. So, this means that it is 55 degree.

To check, if we check 55 plus 125, then 180 is coming. This means that both of these are forming a linear pair on the side of A. So, the sum of both of these is also coming correctly.

So, E and A, both of these are equal. Corresponding angles are equal. All right. and angle A will be equal to angle C, either say like this, vertically opposite, or say like this, or you can say that, what can you say, if you want to find angle C, then F, Corresponding is C. Both are made on the lower side.

Both are made on the lower side. So, F and C will be equal. When a parallel line is transversal cut, F and C will be equal.

F's value is 55 degree. So, C will also be 55 degree. This is the method of doing it.

Tell the teacher the reason that Corresponding angles are equal when transversal cuts the parallel lines. So when a transversal cuts the parallel lines, Corresponding angles are equal. So this was the method of attempting this question. This type of question can come in the exam. Children, keep in mind that if it comes, then it is a 3-mark question.

ok, let's see the next question what is said in the next question in the next question, I have been given a figure again and what is said is, find the value of x in each of the following figure if L is parallel to M if L is parallel to M understand this thing If L is parallel to M, then I have to find X. Here you are seeing that Sir is 110 degree. So this will be the vertically opposite angle.

This will also be 110 degree. Sir, this is transversal. So transversal means that it is cutting parallel lines.

This means that that interior angles on the same side of transversal, both of these have sum 180 degree. If this is 110, then this is also 110. And 110 plus x, means 110 plus x will give 180 degree. Write the reason.

What will you write in front of the reason? Angles on the same side of transversal are supplementary. You will write this reason.

Angles on same side of transversal are supplementary. I am repeating these properties again and again because you will remember them well and understand them. Okay, so pay attention to this. In future, this chapter is not finished yet, it is just the beginning.

8th, 9th, 10th chapter is very useful. These things, these properties called angles are very useful to you. So 110 degrees plus x is 180 degrees. What is the value of x?

The value of x will be 180 minus 110. That means 70 degrees. So we saw that the value of x is 70 degrees. This is one figure. Let's come to the second figure.

Here also we have to find x. Now if we have to find x here, then you see directly, here you are given this figure only to rotate. Rotate means that you get confused that this is 100, this is 80, then how will this x be calculated? You just have to keep in mind that in the question, L is said parallel to M.

L parallel to M. If these two lines are parallel, and this line, These two parallel lines are being made as intersection points They are different intersection points That means this line will be called as a transversal line And in transversal line we have read that The corresponding angles See this angle is made outside Similarly this angle is also made here So these are the corresponding angles. You don't need to use this 80 degree angle. This is just for the teacher to use. You can see this question in 1 or 2 marks in the exam.

If this is 100 degree, then write the value of x clearly in front of you. Don't think too much. Write it straight 100 degree.

And write the reason below. Because if L and M are parallel, then A is transversal. Write the reason here. A is a transversal.

Give reason for everything. If A is transversal, then corresponding angles are equal. are equal and corresponding angles are equal only when parallel lines are there. So, because parallel lines are there, A transversal will be there. So, we saw that as soon as A transversal is there, this transversal has no work and this 80 degree has no work.

This is just a figure to rotate. So, these are parallel lines and this is transversal. So, these corresponding angles will be equal.

This is the story and nothing else. Clear hai bachcho. Toh ye question bhi aap logon hai dekha ki kaise attempt karna hai.

Chapter number 5 NCERT ka exercise 5.2 aap log dekha hai. Question number 4. Clear hai bachcho. Next question dekhte hai. Next question mehme kya diya hai.

Kya aur questions hai mehme pass? Yes. Dekhe ka question number 5. Kya?

In the given figure the arms of two angles. Um. The figure given to you, you can see two angles in it.

And the arms of both the angles, what are the arms called in the angles? Arms means hands. Okay. What are the hands called?

Hands of the angle. What are the arms called? These two lines are called arms.

Okay. So here you can see two angles. One angle is of 70 degrees.

Clear. And the second angle, if you see, this is D. This is the second angle. And this angle is not clearly shown to you. Only 70 degree is mentioned here.

So I can see two angles. What are those two angles? Those two angles are... Hold for 2 minutes. There are two angles 70 degree and here nothing is given.

One angle is given. Angle B and angle E. So, these are angle B and angle E. These are the two angles whose arms are being discussed. What is given further?

In the given figure, the arms of the two angles are parallel. Now, the word is written parallel. Pay attention to this.

Which arms are parallel? Pay attention to this. This arm is one. This is parallel to this arm. Because the arrow is made, so pay attention that it is talking about these two arms.

What is said ahead of us if angle A is 70 degree. If this angle is of 70 degree, then you find the angle DGC. Where is DGC given? See, we highlight it a little bit.

Where is angle DGC given? D, here is D and this point is G and this is C. Is it clear?

So, it is an easy question. See, these two are parallel lines. This transversal is cutting parallel lines.

B will be transversal. See, let's write given. What is given? We are given that A, this line A is parallel to DE. Now, this means B is transversal.

Therefore, B is transversal. Because both these parallel lines are being cut by this line. It's done.

Angle AG. This is 70 degree given. To find, what do we have to do? We have to find angle DGC. Ok, tell me, you must have understood.

See, if this angle formation is happening here, then the same angle formation is happening here also. Let me show you clearly, where I am saying. This angle and this angle.

This angle and this angle, if this is a parallel line and if I pull this line and this line and this becomes a transversal, then the figure in front of you looks like this. ok, two parallel lines are being cut by a line cutter this is transversal and in transversal lines when two parallel lines are cut by a transversal then corresponding angles are equal so this angle's corresponding is this means angle 70 degree and angle G will also be 70 degree so here how you will write statement then As we know, as we know and what we know that corresponding angles are equal when transversal cuts parallel lines. Clear hai?

Now, iska matlab therefore, angle B, angle A, B, G is equals to angle D, G, C. Which is equal to 70 degree. So this is your answer for the first part. This is the way to solve the first part. In the second part, they asked you about the angle DEF. In the figure, see where is the angle DEF.

Let's roughen the figure. Let's see D, E, F. This is D, E, and F. So, we have to tell this angle. It is clear. Now, pay attention how we will solve this.

Can we assume that if this angle is 70 degree, then this means this angle is vertically opposite to the angle 70 degree. If this angle is 70 degree, then alternate interior angles are also equal. So this angle will also be 70 degree. Pay attention here, we will do it here.

Here I am telling you that see the question in the section, A is also parallel to D. So, what we will write is that angle DGC which we have found, angle DGC, keep looking in the figure, angle DGC is equal to angle DGC is equal to angle BGE. Vertically opposite angles, we will give reason, vertically opposite angles, clear? So, vertically opposite angles are equal.

Now, therefore, here you will write therefore, angle BGE, Therefore, angle BGE is equal to angle, which angle is it? Which we had to find, it was DEF or GEF. So, take GEF or DEF, it will work, it is the same thing.

So, here we will write angle DEF. This is the angle. And angle DEF is calculated and that is angle DEF is equal to 70 degree.

This is your second answer. So, here we have to give reason for vertically opposite angle and here we have to give reason for alternate interior angle. The reason for this is this case of alternate interior angles.

So this is the way to solve some questions. Question no. 5 is a good question from NCERT book. You may get to see this in exam.

Let's see if we have more questions. Yes, we have more. In question no. 6, Here are 4 parts in NCIT, 2 are in front of you, look carefully. In the given figure, these 2 figures are given to you.

Decide whether L is parallel to M. Now you have to tell, they did not say anything. So you should remember that whenever we cut a transversal to any parallel, first I will explain, I have explained in theory also. If we cut a transversal to any parallel, So we learnt three things here.

What were those? Those three things were that always corresponding angles are equal. Always alternate interior angles are equal. And the angles which are interior on the same side of transversal. Means this angle and this angle's sum is supplementary.

Means these two angles are called supplementary angles. So we understood these three things. Now we will discuss those three concepts. use here and prove that if we will go in reverse if these three things one of the things will be justified here then we will say that L is parallel to M so we will prove two lines parallel this is a very good question question in three marks or two marks you can see any one part so see how we will do this question I have to decide whether L and M are parallel or not. You will get two angles 126 and 44. First add both the angles.

126 and 44. If I add, I will get 10. 10 has 0, carry 1, 5, 6, 7. So, the sum of these two angles is 170 degree. That means, if the sum of these two angles, if the sum of these two angles, these two angles which are given to you, if the sum of these two angles were 180, then I would say that these alternate, sorry, these angles on the same side of transversal, angles on the same side of transversal are supplementary. If the sum of these two angles were 180, but now it is not coming.

Now it is not coming, now it is 170. So, I would say that no, In this case, I will say no, L is not parallel to M. Why? Give me the reason. Because the interior angles are on the same side of transversal.

If you want to write the reason, then give me the reason. If this question gets in 2 marks, then you have to write the whole reason. I gave the answer of 9. If they ask me here why. and if he give me a question in this 2 marks now this is a question of 1 marks that you decide so I decided no if he ask me the reason why he ask me the reason then this is a question of 2 or 2.5 marks in this case reason de na padta kyunki mujhe jo figure mein alternate mujhe figure mein jo 2 angles dekh rahe hai on the interior angles the 2 angles the 2 interior angles main yaha pe likh deta hu aap log ko reason interior angles on the same side on the same side of transversal are not supplementary are not supplementary angles. This is the reason for this.

So I have given the reason and told you the word no. Why? If you want to write and show, then you can write below this line that angle 126 plus angle 44 is equals to sorry, angles don't come, it has degrees.

Here will be 126 degree plus 44 degree. This will be your 170 degree. supplementary nahi hai. The yeh ho gaya reason, jawab ho gaya, 1 marks or 2 marks ka question ban sakta hai.

Now question number Next, we will see the second part of this question number 6. Are these parallel lines? Which two lines? L and M.

Okay. It is visible that they are not parallel. But, since we have given it a curve, then we will see how to solve it. Okay. Let's see.

I will clear the board first. I had told you the first part. Now, I am telling you the second part. Pay attention.

Here, this angle, the corresponding angle of this is parallel. If it is 75 degree, then this should also be 75. And when does this happen? Corresponding angles are equal when the line is parallel. Okay.

So, if this line is parallel, it is not visible in the figure. But then also, I am checking. Okay.

If it is 75 degree, then this should also be 75 degree. because corresponding angles are equal in parallel line. And if it is 75, then this line is straight line. On this line, these two angles should do linear pair formation.

See 75 plus 75 is how much? 25 plus 75 is 40 and 50 is 150. But to tell linear pair, 180 is there. Linear pair is from 180. So, it means that the formation of linear pair is not happening here. It means that in this figure also, the L is not parallel to M.

You have given the reason, children. Okay, this thing is getting understood. Tell in the comment box.

Okay. Let's see the third part of this. What is given in the third part? See, that is the third part.

Let's check the third part too. It has the same question. Decide whether L is parallel to M or not.

If this is 57 degree, See, this angle, angle is being made. What will be its corresponding angle? Sir, its corresponding angle will be this. If it is 57 degree here, then that means it will be 57 degree here also.

If two lines are parallel. If two lines are parallel then these will be called corresponding angles. And corresponding angles will be equal. If two lines are parallel then corresponding angles will be equal.

So 57, 57 is here. And 57 plus 123, check it. 57 plus 123 is how much? When you check this, then it will be 10, 10 equals 0, carry 1, 8 and 1. You saw, These two angles 123 and 57 are supplementary angles.

So yes, here a linear pair formation is happening. This means that this is a straight line. This is a straight line.

Okay. So this means that if this angle is equal to this angle, then these two are giving 180 degrees from the linear pair. So I will say yes. Yes, L is parallel to M. In this case, what will we write?

If this figure comes, what will we write below it? What you have to write below it? Pay attention.

You have to write below this figure. Yes, L is parallel to M. Because, as we know, as we know, that is...

that... Do we know if transversal cuts parallel lines, if a transversal cut parallel lines, then corresponding angles are equal. We know this. And in this case, what is this thing that is visible?

So we will make a drawing below this. This is the drawing. It is cutting a line. This angle, because we were given 57 degree, so this angle will also be 57 degree. Okay?

And here is the formation of linear pair. So write that too. Linear pair according to linear pair concept. According to linear pair property 123 degree plus 57 degree is equals to 180 degree. So, it means that 123 plus 57 equals 180 degrees.

We can see that here. This is the angle of 123 degrees. So, because of this, we are calling L as parallel to M.

Because all the things are being proved here. So, we can see that L is parallel to M. This is one thing. So we have seen the third part of question number 6 In the other two parts, the first and second were No and No In this case, Yes is coming In this, fourth part is also given Let's consider this as a view If this is 98 Then this angle The sum of both of them This is transversal So interior angles on the same side of transversal are supplementary angles. Clear?

We know this thing. So, 98 plus this angle. How much is this angle? This is its vertically opposite angle. This means this angle will also be 72 degrees.

So, here 98 plus 72 is how much? See, 8 plus 2 is 10. 10 has 0. Carry 1. 10 plus 7. So, this will be 170. So, here see that the sum of these two is 170. 180 is not coming. If 180 comes.

So, I would say that L is parallel to M. So, in this case also this condition is wrong. That means we will not say that L is parallel to M. In this case we will say no.

Which case is this? This one. And for this case, my answer is yes. Is it clear, kids?

So, this is the way to decide something. That two lines are parallel or not. If two lines are parallel, are of each other, then three conditions should be justified. OK, out of those three, if any one condition is justified, we will say that two lines are parallel.

But in this case, we saw that nothing was being justified, only one option was like this, the third one, we were given four figures in total, only the third figure was such that was justifying this case. That is why we said here that L is parallel to M, we said no, no, no in the rest of the So, kids, you understood till here. Let's see, we have more questions. No, so kids, you stay with us.

Here we have finished the exercise 5.2 of NCRT. In my next video, I have come with some more extra questions. Which I have picked from book R Sharma. And I think... I think teacher should give you these questions watch my next video to see those questions and stay tuned with us on magnetbrains.com here you are getting free education from kindergarten to class 12 bye and take care