hello students welcome to my channel my name is dasan I'm your Mets Prof so here we are starting the third chapter that is lines angle and shapes and uh in this chapter there are these uh six topics uh we'll be covering uh so as you already know that we have this uh uh you know method that we first you know uh explain each and every topic with you know small small uh examples of each and then uh there will be separate sessions for problem solving where we'll you know solve uh worksheets Bas on based on this third chapter so there'll be six different uh sessions based on the six topics where we'll cover each and every topic in detail and uh then we'll see the paper two style questions and paper four style questions okay so let's start the first topic this is angles so angles if you see if I classify the angles angles are classified like this uh acute angle acute angle means an angle uh which is measured less than 90° less than 90° is called acute angle so if I sketch an acute acute angle it looks like this uh let let me just make it you know clear so it's something like this it's smaller than 90° you see then comes the right angle right angle means exactly equal to 90° so if you sketch it it looks like this somewhat like this yeah and uh we we we you know uh specify it we we show it as uh you know Square which signifies that is a right angle then there's an obtuse angle obtuse angle is when it is between 90 to 180 between 90 to 180 is called acute angle sorry Opus angle so it looks like this here so this is an obtuse angle then comes the straight line straight line is exactly 180° so it looks like this it's a straight line and this angle is 180° then comes the ri Flex angle which is between 180 to 270 sorry between 180 to 360 I mean that's between 180 to 360 so it looks like this and this outer angle is a reflex angle and then there's a complete angle complete angle means 360° so it's just one Ray and this whole angle is 360° that that's a complete angle so this was the classification of angles you must have you know uh learned about it in your pre uh you know primary grades uh it's just the revision of that then uh what are the pair of complimentary angles pair of compliment angles means uh when two angles sum up to 90° so let's say there are two angles one is Alpha and another is beta so if Alpha plus beta sum of two angles is equal to 90° then that Alpha and beta form compliment pair so this is complimentary pair and pair of supplementary angles supplementary angles means two angles whose sum is 180° so Alpha + beta is equal to 180 then Alpha and beta form supplementary pair clear so supplementary is uh total 180 and complimentary is total 90° I hope this is clear y now let's see when two parallel lines if you see this let let's call this L and this m two lines and they are parallel to each other we can show it like this so they are parallel to each other and there is a line n which is uh intersected which which intersects both l and m both so it is called transversal line these two parallel lines and there is a transversal line n so whenever two parallel lines are intersected by a transversal line in that case these eight angles are formed you see A B C D E F G H I have named them A B C D E F G and these eight angles are formed now we'll see how many different kinds of pairs are formed here okay yeah uh let's first see the linear pair linear pair is basically uh you know a pair of angles which are on a same straight line if I see uh if you see this this uh line L Line This is line L and this angle uh angle a and angle B they are on the same line right and they sum up to 180 because they uh are on the same line so if you add them it will be a total straight line so that will be total 180 similarly this B and C they are also linear pair because they are also on the same straight line that line is n this is L uh this is M and this line is n so linear pair is a you know a pair of angles which are adjacent to each other and they are on a straight common line one straight line so they are called linear pairs so let's write all the you know linear pairs here and by the way they add up to 180 so we can say that linear pair is always a supplementary pair supplementary means they add up to 180 clear so let's write all the linear pairs here angle a and angle B if you see they they form a linear pair because they are adjacent to each other they have a common arm this and they add up to 180 they are on a straight one single straight line similarly uh angle B and angle C they are also linear pair angle C and angle D similarly angle D and angle a these four pairs of linear uh you know uh these four are linear pairs which are on the same line L similarly on line M you see these four angles out of these four angles the pairs are like this angle e and angle F then angle F and angle G same like the above one uh angle G and angle H as well as angle H and angle e so these are the pairs of you know linear pair basically so they add up to 180° clear next is vertically opposite angles vertically opposite angles basically the angles they form X here if you see these A and C are opposite to this uh when the x is formed uh X shape X of the you know alphabet English alphabet uh and this A and C are vertically opposite similarly B and D they are for pair of vertically opposite angles then e and G pair of vertically opposite angles as well as F and H and vertically opposite angles are always equal okay so here I'm writing angle a and angle C they form vertically angles pairs angle B and angle D similarly angle e and angle G and angle F and angle H so there are total four pairs of vertically opposite angles and they are equal to each other so angle a is equal to angle c angle B is equal to angle d e is equal to G and F is equal to H next uh is uh pair of corresponding angles corresponding angles are uh you know the angles which are at the same position on two parallel sides so if I see here angle a and angle e they are on the same position but on two different parallel lines similarly B and F are also at the same position similarly C and G are corresponding and d and H are Cor corresponding and uh a pair of corresponding angles they are equal to each other the angles are equal to each other so I can say that angle A and E are equal B and F are equal D and H are equal similarly C and G are equal so I'm writing here uh the pairs are angle a and angle e then angle B and angle F similarly angle C and angle G and angle angle D and angle H okay you are supposed to remember all of these uh if you uh you know maybe in the first trial if you can't remember just revise the video again and again and uh uh it will be easier for you to you know remember then the alternate interior angles now if you see uh in these eight angles out of these eight angles this four d c f and E these four are interior angles and this a b g and H they are exterior angles so out of these four interior angles if I take a pair of alternate uh interior angles so they are angle D and angle F so basically on the opposite side and they are interior similarly angle C and angle e sometimes we uh you know for uh easy to remember we remember it as Zed uh you know English alphabet Zed so this D and F they are on the opposite side of Zed similarly there's you know uh inverted Zed like this so This c and e are of the opposite side of that Z so they are alternate interior angles and they are equal to each other alternate interior angles are always equal clear then comes the co- interior angles out of these four interior angles only if you see the co interior angles means interior angles on the same side so this D and E are Co interior angles similarly C and F are co- interior angles and co- interior angles are supplementary so they add up to 180 supplementary so here I'm writing both the pairs first is angle D and angle e similarly angle C and angle F so I can say that D+ e is equal to 180 as well as C + f is equal to 180 okay now comes the exterior angles as I already told you these four are exterior angles a b g and H out of them if you want to write the alternate exterior pairs alternate exterior pairs are this A and G which are on the opposite side as well as B and H they are also on the opposite side and they are exterior also and alternate exterior angles are equal same like alternate interior angles alternate exterior angles are also equal so this angle a and angle G alternate exterior angles similarly angle B and angle H they are also alternate interior angles and alternate interior angles are equal to each other then the last one they are Co exterior angles sorry I uh this is alternate exterior not alternate interior they're alternate exterior and they are equal to each other then comes the co exterior angles Co exterior angles are exterior angles of the same side so this A and H alternate exterior B and G alternate exterior and alternate exterior angles are supplementary same like alternate interior alternate exterior are also supplementary supplementary means they add up to 180 so here I'm writing angle a and angle H alternate exterior angle B and angle G alternate exterior so they add up to 180 a plus h is 180 and B and G B+ G is 180 clear so we saw a pair of alternate exterior angles which I have written here then there are uh sorry Co exterior angles alternate exterior angles then alternate interior co- interior corresponding angles vertically opposite angles and linear pairs so try to remember all these Pairs and once you remember all of them it will be very easy for you to you know solve the questions based on this u a pair of parallel lines and there is a transversal line also clear let's see some questions uh I've taken few examples from the uh igcc textbook course book only um see the first one here we are supposed to find X and Y so you see Y is vertically opposite of 57 and vertically opposite angles are equal so I can directly say that Y is equal to 57 and every time you are supposed to write the reason also so here I'm writing the reason in shortcut that v o a vertically opposite angles but in the exam don't write the shortcut uh you know write the whole thing vertically opposite angles clear so Y is vertically opposite angle this is why it is 57 similarly this Zed you see Zed and 121 they are on the same straight line so they add up to 180 because they form linear pair yeah so x + 121 is equal to 180 reason is linear pair here I'm writing in a short form but don't use the short form in the exam so X is = 180 - 121 that's easy that is [Music] 59 clear so so this is how I found X and Y both let's see another example huh so here uh this 82 X and 82 they are not a pair basically they're three angles so we cannot write the form linear pair but of course they are on the same straight line so they add up to 180 because if you add them it will be a straight line only so here we can write it like this 82 + x + 82 is equal to 180 but the reason will not be linear pair because linear pair means two angles only it should be a pair but here it is not a pair there three angles they Trio so for that we'll write just straight line reason is just a straight line okay now 82 + 82 just make X as a subject so 82 + 82 is 164 + x is equal to 180 make X as a subject this 164 goes in the subtract ction so it will be 180 - 164 so that is uh 16° yes so X is coming 16° now you see this x and the Zed they for they are forming X and they are opposite side of each other basically vertically opposite angles and vertically opposite angles are equal we have already learned about it so X is equal to Z reason vertically opposite angles and X we have already found that is is 16 so Zed is also 16 right now y uh you see Y is a vertically opposite angle of 82 H so because this is a this x is form now and they are opposite to each other so 82 and Y must be equal so Y is directly equal to 82 reason is vertically opposite angles so x y and Zed we found next example uh this X 90 and Y they form the total straight line but there are two unknowns so first let's find one of them uh and then we'll find the Y also so see this X and 47 they're forming vertically opposite angles vertically opposite angles because they form X here and they are opposite to each other so X is directly equal to 47 reason vertically opposite angles as you already know vertically opposite angles are equal now similarly uh let's find the Y X plus this 90 plus this y they add up to 180 because there's a single straight line here but you cannot write linear pair because there are not two angles there are three angles so x + 90 + y is equal to 180 but the reason is a straight line okay so we have already found X that is 47 + 90 + y is equal 180 and let's make y as a subject first of all this 47 and 90 they add up to 137 + y is equal to 180 and to make y as a subject will uh you know throw this 137 here opposite side of the equal to sign and it will become minus 137 so 180 - 137 that is 43 clear so so Y is coming 43 now you see Zed now many students make this mistake they uh they find that Zed is equals to 90 because it is vertically opposite but you see 90 and Zed are not vertically opposite because they are not forming X there you see this is one line and there is no other line there are two lines so they are not forming X so don't write it as vertically opposite angles but instead this Zed and 47 they add up to 180 they form a linear pair because there's a straight line okay so Zed is not 90 don't make this mistake I've have seen students making this kind of small mistakes so every time when I see any you know repeated mistakes made by my students I'll always point it out so this Z + 47 is equal to 180 make Zed as a subject so that is 180 - 47 and here yeah reason is linear pair so 180 - 40 47 if you see that is uh uh 133 clear okay so that's all let's see the another example yeah so here if you see the total is 90 right so if you add X and 19 the total is 90 sorry for the blur image we I've taken the screenshot so of course the image will be blur but it is visible so that's fine so x + 19 is total 90 and the reason is complimentary pair at the starting of this session Ive you know told you what are compliment Pairs and what is supplement pair so this X and 90 they are forming a complimentary pair so let's make x a subject so that is 90 - 19 so that is uh 71 so X is coming 71 next another example you see X 2X and 45 they all add up to 90 but here don't write complimentary pair because they are not forming a pair they are three Tri three angles so basically it's a trio it's not a pair so x + 2x + 45 is equal to 90 and here you don't need any reason you can just write it's a given in the diagram that they add up to 90 so you see x + 2x we want to find the value of x so that's x + 2x is 3x like terms and just throw this 45 on the opposite side of equal to sign so it will be 90 minus 45 that is 45 only and then this three will be thrown in the division so 45 / 3 x is 15 so the value of x is 15 clear let's see the last example you see here these two lines are parallel to each other right if they are parallel to each other then we have already seen those eight kinds of pairs uh what are them let's let's just revise them first is linear pair which are supplementary then vertically opposite angles they form X and they are opposite to each other they are equal to each other then there are uh corresponding angles which are at the same position uh on two different parallel lines and they are equal then comes fourth one is uh alternate interior angles they are equal they form Zed that English letter Zed then uh co- interior angles uh they add up to 180 so they are supplementary then uh Co exterior angles similarly uh they are supplementary and vertical sorry not vertical exteror angles of uh alternate exteror angles basically so they are equal to each other so all these are the pairs which we have already seen so let's find using that uh you know concept this y I and 60 if you see they form Zed and two lines are parallel also the lines must be parallel then only the alternate interior angles are equal H by the way so Y is equal to 60 directly we can write and the reason is alternate interior angles so this is how you found the value of y similarly this this X and 45 they are also forming the pair of alternate interior angles and two lines are also parallel so we can directly write X = to 45 same reason alternate interior angles clear oh I have another one see this it's not a pair of parallel lines but there are three lines which are parallel to each other okay so let's use all these uh same kind of uh concept first you find uh this D because it's a linear pair of 105 they are on the same straight line okay so I'm writing 105 + D is equal to 180 reason is linear pair so d is0 - 105 and if you do 180 - 105 that is 75 so D is coming 75 then similarly this 40 and a they are alternate interior angles and these two lines are parallel also so a will be directly equal to 40 reason is alternate in interior angles clear now this uh b and a they form a linear pair so A + B is equal to 180 reason is linear pair they are on the same straight line so a we have already found 40 + B is equal to 180 so let's make b as a subject that is 180 minus 40 180 - 40 is 140 so this is how you found B now e and C are left now forget about this line but this 105 and E they are corresponding angles because these two lines are parallel to each other and they are on the same position on two different parallel lines so they are corresponding angles and corresponding angles are equal so e is directly equal to 105 reason is corresponding angles sorry H so that is corresponding angle Les now only C is left now C and D are corresponding because these two are parallel lines and they are on the same position so C is directly equal to D same reason corresponding yeah so and D we have already found that is 75 so c will also be equal to 75 clear so here in this session we we saw uh basics of uh uh angles and what compliment pairs what supplementary pairs then we saw uh then then we saw the seven different types of pairs formed when two parallel lines are intersected by a transversal line clear in next session we'll see uh the second topic of this chapter that is uh angles in a triangle till then just keep practicing and uh keep revising this topics all the playlist will be there in the channel and keep supporting the Channel please like the video and share it with your friends those who are in the igcc and in next uh you know uh week from the next week I'm starting ibdp uh maths sessions also uh they are also you know uploaded in this same same um Channel but uh there will be a separate playlist for it thank you so much