Chapter 3: Angles

hello grade 8 children today I'm here to teach you chapter 3 in your textbook that's angles this is a geometry lesson we'll see what are the basics related to angers what is an angle so angle is formed by two line segments from one center point so if we take this point oh oh a OB are the two lines so here we can say Oh a and OB pass from the center point oh oh is the vertex point we call this is the vertex point and it is fixed and Oh a and OB ah raise angle is what is the angle form we can write two ways we can start from a a OB so this is how we write a OB and we put a hatch above representing that o is the angle or we can start from the other side B or a so we can write like this or if it's one angle we can write down just a anger this is also possible so when you take this diagram you get two line segments and a fixed point so we can define angle as a rotation so how we can define an angle as a rotation rotation of a line segment what is the line if you take this one Oh a is the line segment around the point oh it's called the anger so when you rotate here to here you get an anger so this is the angle created and this is clockwise we are rotating clockwise from a units off angles what are the measurements we use we used degrees how we represent degrees so we put a small 0 so here superscript of 0 so if this is 30 degrees we put 30 and put a small 0 here so this means 30 degrees so you need tough measurement used for measuring and angle is decrease symbol for degrees is a small circle in the superscript so if you take the circle the entire circle so how many degrees is that so 360 so entire circle is recognized as 360 degrees so here can you see the degree sign 360 degrees starting angle at always zero because this is not rotating so here starting angle is zero degrees now we'll rotate half of a circle so this is the fixed line and starting from the fixed point or 1/4 of a circle we know the full circle is 360 so 360 and 1/4 of that what's the angle you'll get 90 degrees so this is 90 degrees normally we represent this angle as ur a square like this so that means this is 90 degrees then rotation of half of a circle so here to here is half of 360 so you get 180 degrees what about this one 3/4 so when you divide the circle into 4 parts this is starting from here 3/4 of a circle full circle is 360 3/4 of that 3/4 of 360 what's the value for x this 990 times 3 270 so this is 270 decrease so what are the types of angles that we need to learn so first one is acute angles what is that cute angle so the angle in between 0 and 90 degrees so less than 90 degrees and above 0 degrees is called acute angle right angle so right angle is 90 degrees so we represent using a square like this then obtuse means the angle is more than 90 degrees so here if this is 90 degrees this is more than 90 degrees and less than 180 degrees so we call it as obtuse angles what is straight angle means if the angle is 180 and this is a straight line so GFP is a straight line if it's a straight line we call this angle is a straight angle 180 degrees and you need to know another type of angle that's reflex angle reflex angle is angle above 180 so this is 180 line above 180 and below 360 so this is the 360 degree line so you can get either this type of angle oh yeah more than 270 also possible so this is up to here that's 270 so this angle is more than 270 as well so these two are called reflex angles or cheese and angles what are just and angles so angles e OB and b or c or c OB b or c adjacent angles in the above diagram so what are the properties in adjacent angles common arm is there so two these two angles this is the common arm one fixed line is there so that's Oh big you need to get a common vertex point so this is the vertex file so what's the vertex here Oh Oh vertex point and angle situated in opposite sides of the common so common arm is here so this sandal is anti-clockwise and this angle is clockwise so angle situated bow in both sides so these are the three properties satisfied for adjacent angles now identify in this diagram what are adjacent angles look at this o P lie when you take Opie line that's the common arm from here there's an anger anti-clockwise what's the angle P o our reflex angle P you are this is the reflex angle Modell's 180 and less than 360 and what's the other angle this is clockwise measured this angle P or Q so P or Q and P or our reflex angle ah adjacent angles with common arm o P so what's the fixed point here or is the vertex point look at this one identify what's the common arm and what are the two adjacent angles so when you look at this diagram we can see this is the common arm o our common arm and what are the two angles from this this is one q or r QR or you can write R Rho Q and what's the other one this one so we can write P or our reflex angle so these are the two adjacent angles in this diagram what's the common now we can see common arm is o Q and what are the two angles this one here measured anti-clockwise p or q p oq' angle and what's the other angle Q or are these are adjacent angles with common arm or Q and what's the vertex point vertex point is o what are complementary angles two pairs of adjacent angles add up to 90 degrees we call those are complementary angle now take a look at these two this angle is 60 degrees and this is 30 degrees so what is 60 degree angle plus 30 degree angle you get 90 degree so the sum is 90 degree so we can say a Obi angle and P or a angle ah complementary angles because the sum of the two angles is equal to 90 degrees write down the complementary angle to the given angles thirty's there how you find out the other girl 90-30 that's 60 degrees 50 if one angle is 50 what's the other complementary angle you subtract 50 from 90 you get 40 degrees 85 90 minus 85 that's 5 degrees 24 90 minus 24 you get 66 degrees 36 90 minus 36 but you get you get 54 90 minus 36 and what about 3 degrees 90 minus 3 degrees you get 87 so these are complementary angles look at this one ninety degrees and zero are not complementary angles zero angle does not exist so don't take 90 and zero those are not complementary angles complementary adjacent angles so complementary means add up to 90 what are adjacent angles adjacent angles you need to have a fixed point vertex point comma Nam and the two angles to ated on both sides of the common Nam now look at this diagram you can see when you add a abd angle and DBC angle what's the sum this angle and this angle you can see is 90 degrees so that means these two angles are complementary now why this is complementary adjacent angles so when you take this diagram this is the common arm and this is the vertex point and this angle measured this way anti-clockwise this angle measured clockwise so the two angles on both sides of the common are so these are complementary adjacent angles supplementary adjacent angles supplementary means the sum of two angles add up to 180 now look at these two C B a or ABC and abd so what are the two angles 110 l70 so when you add it you're getting hundred eighty so we call two angles equal to 180 are supplementary angles and these are also adjacent when you take this common arm a B so when you take this slide on top of this line you're getting an angle like this so this is the BD lie so you can see Oh a is the common ah and this angle measured anti-clockwise this angle measured clockwise and this is the fixed point B so two angles equal to 180 are the supplementary angles and you can say a b c and a BD we are supplementary adjacent angles because when you take it together you get adjacent angles as well write down the supplementary angle to the given angles so what's the condition the sum is equal to 180 if 40 is the angle 180 minus 40 is the other supplementary angles that's 140 8500 80-85 mercy angle 5 and 1 remaining so that's 995 60 degrees 180 minus 60 that's 120 degrees 75 watts the supplementary angle 180 minus 75 you get Conrad 5 117 so subtract 117 from 180 63 degrees 29 you get all these are angles this is 29 so subtract you get one here and here subtract from 181 there and this is three so five 151 so these are the supplementary angles so what are supplementary angles the angle sum is 180 supplementary adjacent angles means we did that before so the sum is 180 as well as the two angles are adjacent now look at this guy Group abd is haunted DBC is 70° so when you add it you get 180 decrease so these are supplementary adjacent angles because when you take this is the common arm BD and the common vertex vertex is B and the two angles measured both sides those are the three properties for an adjacent angle now we look at what our vertically opposite angles now look at this one a B is a lie and C D is another line straight lines so intersect these two lines at O this is the intersection point so you get four angles there one two three four four angles and here's shaded once what are shaded ones e OC and the other one B OD a pair of vertically opposite angles so here this is one angle and this is the other vertically opposite angles now when you look at other way around this is also vertically opposite angle so what are the other unshaded Part A or D aug angle and be your C angle these are another pair of vertically opposite angles so how we get vertically opposite angles when you get any two straight lines intersecting each other now two lines are there pql SR so identify a pair of vertically opposite angles in the above diagram we can say this and this our vertically opposite angle so here P o R and s o Q angles are vertically opposite angles what are the other two this angle with this angle so you can write P o s angel' and Q o our angle is also vertically opposite angles so you get two pairs of vertically opposite angles now one angle is given eighty degrees a OD anger so what's a or C angle we know C D is a straight line so what's the angle so if this is straight line this is a straight angle 180 so 180 minus 80 a OC angle is 100 a or D angle is 80 and also this is a straight line a B is a straight line so what's this angle this angle that's B or D angle B your J angle is also 180 so I can write a OD angle plus D B or D angle it's 180 so this is also 100 degrees so this is hundred that's B oh t angle so I can write B or D angle is hundred degrees now look at carefully this and this what can you say a oh D that's a or c a.o c and b or g angles we know that these are vertically opposite angles and also they are equal so remember the two vertically opposite angles now I can write a Oh C and B or D vertically opposite angles are equal similarly what can you say about the other one this is 80 this is also 80 so we found out this is also 80 so what's that B oh see anger so similarly I can write a OD and be your C angles are equal that's 80 degrees so we can say vertically opposite angles are equal this diagram identify vertically opposite angles that I equal POS POS is here what's the other vertically opposite angle this one Q or R if you take P or P o R naught P Q R this is P or R P o R is equal to this angle so that's Q or s so these two are vertically opposite angles find the values of a B and C what can you say about a angle can you see this is a straight line so a is 180 minus 100 because this is a straight angle so what's the answer eighty degrees then what you know about C angle E and C both are equal because those are vertically opposite angles so is 80 that means C is also 80 vertically opposite angles then what about B B and 100 these are two vertically opposite angles so we can say B is also 100 degrees because of vertically opposite angles this diagram find the values of P Q R this is 70 so this is a straight angle so what's be 180 minus 70 that's hundred check so we can write that's because of straight angle then you can write P is equal to R so this is hundred ten because of vertically opposite angles seventy and Q is also vertically opposite angles so Q is equal to 70 these two are because of vertically opposite angles now we look at angers around a point so the fixed point here is o so when you take from here around this point we know that the sum of angles add up to 360 degrees so here we can write all these angles so what are the angles X Y Z and this sandal is a all these angles add up to 360 degrees so when you get a point make sure that the sum of angles add up to 360 degrees find a and B so this is the fixed point so this is also around a point so how can we find out a now when you take this line this is a straight line this is 90 given here to here straight angle here to here straight angle because this is a straight line so what's a is 180 minus 90 degrees because this is given as 90 degrees so that's 90 but we know the angles around a point is 360 so what's big B is 360 minus all three angles so here what are the three angles 90 a is 90 and 100 so when you add it you get 280 degrees 280 degrees is the other three angles so what is B 360 minus 280 so what's the value 8 so B is 80 degrees look at this one this is a point so we can consider angles around a point to find out the value of a 60 plus 80 plus 80 what's the sum 220 and all the angles add up to 360 so what's a it is 360 minus 220 what's the answer answer is hundred forty degrees find the value of x here what can you say about this one this is a straight line so what's this angle straight angle so X plus X plus X is 180 because of straight angle then X plus X plus X is 3x is 180 divided by three you get the value of x so x equals 60 degrees you have given several angles and identify types of angles so acute means the angle less than 90 degrees 30 degrees is then an acute angle what are the other angles less than 90 55 68 84 forty-eight loser accurate right angle means 90-degree angle obtuse obtuse means more than 90 less than hundred eighty degrees hundred twenty hundred forty 170 hundred twelve what is less than hundred eighty visa more than 180 straight angle means equals two hundred and eighty so I can take 180 degree n then what are reflex angles reflex angles are more than 180 and less than 360 so 270 195 200 and 318 those are the reflex angles you have given several angles and you are asked to write down pair of complementary angles complementary means the sum add up to 90 degrees what are the angles add up to 90 degrees look at 70 and 20 at up to 90 degrees so you can write a b c and k l so these are complementary angles add up to 90 degrees and write down the pair of supplementary angles what are supplementary means add up to 180 this sand that's 150 plus 30 you get 180 so x y z and c d e are supplementary angles because these are add up 280 identify the type of angles so what is this angle less than 90 degrees acute angle this one more than 90 degrees obtuse this one also less than 90 degrees acute and we look at some more angles this is more than 90 degrees less than 180 no twos angle this one yeah 90 degrees so what you call for 90 degrees right angle this one 180 straight angle this one more than 180 what you call that reflex this is also more than 180 so that's also reflex this is 90 degrees so what is 90 means right angle this is two straight lines intersect at one point so what are these two vertically opposite angles find X in this diagram we know this is a straight line and this is add up to 180 so 2x plus X plus 60 is hundred eighty now take 60 to the other side that means subtract first we'll add these two to X and X becomes 3x and subtract 60 from both sides you get 3x equals 180 minus 60 degrees left 180 minus 60 means 123 X 620 means divide this by 3 you get x equals 40 degrees I'm glad 20 divided by 3 so X is 40 degrees find X in this diagram this is mentioned this is 90 degrees so 2x plus x equals 90 degrees what are those complementary 2 X plus X is 3x equals 90 degrees divide this by 3 you get x equals 30 90 divided by 3 find ABC can you see this one and this one vertically opposite angle so a equals 85 you can write down what the reason vertically opposite angles then B equals what when you take this straight line B equals 180 minus 85 so B equals 180 minus 85 because of straight angle so subtract you get 5 and 9 so 95 is the B value now what is C B and C are vertically opposite angles so we can say see also 95 because of vertically opposite angles a bee is a straight line find ABC so I'll put a bee here a bee is a straight line fine ABC now when you take this three angles a plus 3a plus two ways hundred eighty that's a straight angle so add it together 3 + 2 5 + 1 this becomes 6 8 equals 180 when you divide by 6 you can get there a value so you get a equals 30 degrees now we'll look at this one this side lower side here what can you say about 4 a and B that's also straight angles so before that we'll find out for a is 34 times 30 is 4 that's 120 degrees now what can you say about these two angles these are straight angles so for a and B straight angles so 180 minus 4 is equal to B so you can't just subtract 180 minus 120 that's 60 degrees because these two are straight angles look at this one find y when x equals hundred check so this is given hundred and ten what's the Y value we know this is straight line so Y is hundred eighty minus hundred check so that's 70 degrees find y when x equals 150 if this is 150 what's the relationship 180 minus 150 is why so that becomes thirty and then here find X when y equals forty same thing happens X is equal to again 180 minus the Y value now why is for T you get hundred forty degrees find X when y equals fifty these two are straight angles so you can subtract from 180 so you get 130 there this one this is a fixed point what's 50 and 30 and you shown is 80 this is 80 80 plus two x two x three X is equal to write it here these three angles add up to two x two x three exist have an X and this is equal to what is this 180 degrees so all together is 7x and this is 50 and 30 80 all together what's equal to this is equal to hundred eighty or 360 this is a point 360 degrees so angle at a point angle around a point so what is 7x 360 minus 80 degrees so you can subtract you get 280 so 7x equals 280 so what's what's the value divided by 7 to get the x value so X is equal to 40 degrees so make sure this is a point so angle sum of a point is 360 look at this one it's given a OD AOC b OC the sum is 260 find the values of all four angles so what's this Stanga BOJ angle so b OD angle is 360 it's minus 260 because this is a point and sum of angles around a point is 360 so 360 minus 260 you get hundred decrease that's for B or D then what can you say B or D angle and this angle AOC angle both are equal vertically opposite angles so you can write a OC is equal to 100 degrees so this is hundred this is hundred then how can you find out be your C anger we know a B is a straight line this is 100 so this becomes 180 minus 100 that's 80 degrees now Bo say is 80 means a OD is also 80 degrees that's vertically opposite angles look at this one a B and C D are straight lines intersect at oh this is a fixed point find the value of x what can you say about this angle and this angle these two are equal vertically opposite angles so X and X 2x is equal to 80 degrees so how we find out X divide by 2 so X is equal to 40 degrees find a from this diagram we can first add 60 and 40 is 100 hundred degrees so for a is what this is a straight angle so for a equals 180 minus 100 that's 80 degrees so how you find out a divided by 4 so a equals 20 degrees look at this diagram and find out what's the value of a this is a point so we can add all these angles add up to 360 so 5 + 2 7 7 + 3 10 10 plus 2 12 a is 360 so what's a divided by a equals 30 decrease find X here this is a straight angle X plus 30 plus X plus 20 and 60 and up to 180 now I'd like terms x + X becomes 2 X 30 plus 20 50 50 plus 60 hundred ten now how we find out X so 2x equals subtract 180 from subtract 110 from 180 you get 70 degrees is 2x divide by 2 what you get X is equal to 35 70 divided by 2 is 35 find ABC PQR all these angles this is a straight angle so a is 180 minus 70 so hundred check what's B P is 70 because this and this both are vertically opposite angles B is 70 vertically opposite angles see a and C vertically opposite angles so C is equal to 110 that's vertical same reason this side this is also another point two straight lines are there so straight away you can write P equals 180 minus 150 that's 30 degrees because of straight angle then q q 150 both are vertically opposite angles so Q is 150 vertically opposite angles and what's our R and P both are equal those are vertically opposite angles so our a same as P that's 30 degrees the reason is the same vertically opposite angles a B and C D are straight lines find ABC this is 90 degrees so what's 90 plus 60 on Brad 50 so what's a because this is a straight angle a is 180 minus 150 that's 30 degrees so what's the reason straight angle what's the B value we is 60 degrees what's the reason vertically opposite angles then let's see what can you say about si si is these two lines so this and this a with 90 vota vertically opposite angles so a plus 90 so 90 plus 30 you get 120 vertically opposite angles now we will look at the review exercise so we covered about obtuse acute reflex angles and complementary and what is supplementary angles and vertically opposite angles so now we will see how we can apply those properties in the exercises look at the first question copy the two groups a and B given below and join them appropriately 135 which type of angle it says obtuse angle 90 is right angle 180 is a straight angle 35 is acute angle 245 is reflex angle more than 180 and 990 also reflex angle and 280 also reflex angles by considering the given figure find the magnitude of each of the angles given below and cried the type of each angle a OB a OB is 90 degrees what's the anchor right angle C or D C OD given that that's 40 degrees that's a acute angle B OD which one is B OD b o T that's also 90 degrees that's a right angle and B or C this angle so how can we find out vo C 90 minus 40 90 minus 40 is 50 degrees so that's an acute angle AOC 90 Plus this so this is 50 we found so a oh C is equal to 90 plus 50 so what is ninety plus fifteen hundred forty degrees a OD so a OD is a straight line so 180 that's straight angle look at this one draw the following angles using a protractor and name them so first one is PQ R so what we do we take the ruler and draw a straight line okay and then what we do we take a point P we take the point Q because you have to draw the angle PQR now take the protractor what we do we keep it on top of the point Q and measure the angle so what's the angle sixty degrees from here anti-clockwise we can mark the point so this is the point here 60 degrees so you can move this and draw the line passes through this point and this point so I can draw the line like this so that's P QR 60 degree angle so this is 60 degrees now look at this one ABC is 90 degrees so how we draw the 90 degree angle draw a line and then you can mark the angle here B angle so we'll take any point B now we can measure 90 degrees so take the ruler not the ruler protractor and keep the protractor on top of point B and Misha here you have to keep it properly this one on top of this line so something like this yes still not okay so here make sure that you keep them okay so here now it's correct so keep on top of the line now mark the point 90 degrees from here so this is the mark and you can draw the line now take the ruler connect this point and this point that's 90 degree and so this is 90 degree angle so you need to label this this is a B C so ABC is 90 degrees 130 degrees so what you do take a line and draw the line there and you need to mark a point so we'll take this point is there this so why now we need to measure 130 degrees so take the protractor keep on top of the line and here on this point zero point on Y now from here you have to measure that's hundred thirty so here to here this is 130 mark take the projector away and now you can take the ruler and connect this point with this one then what's the angle XYZ so we can mark this is X Y Z and this is 130 degrees this way is 130 degrees 48 degrees so how we draw 48 so take the ruler and then Mark a point will mark L so this is the point we have to mark that's angle then 48 degrees take the protractor keep on top of this and mark 48 degrees so 48 is here 40 and in between 50 and here so this is 48 now you can connect these two points with a ruler so mark it and then connect label the two points K and K L M angle is 48 degrees question number four as shown in the figure draw two straight line segments a B and C D such that they intersect each other at Oh make sure the magnitude of each of the angles AOC that's this angle C or B this one and B or G this one and a or D so all four angles we need to mission and write them down what is the value of AOC and c OB with first measured using the protractor take the protractor keep on top of this line and you can measure this part so here in your protractor you can measure from this way as well my one you only from this side so I have to subtract this value from 180 so 180 minus 140 so here to here is 40 degrees so I can write a or C angle is 40 degrees then boc angle or c OB angle i can measure from here that's 144 you you can measure from both sides zero is here as well as zero is here so look at carefully and measure the correct way so c OB is an obtuse angle that's hundred forty now a OC with measured co b b OD so how do you do B or D B or D is this way so we need to keep the protractor this way so this way and we can measure here to here that's 40 degrees b OD is 40 degrees here to here you can measure so 180 minus 40 or i can get straight away hundred forty-four a OD angle a OG is hundred forty degrees now what is the value of AOC plus Co be these two AOC is 40 degrees C or B is 140 so when you add these two what you get hundred eighty degrees so those two are 180 degrees are the two angles AOC and b OD equal to each other AOC forty B or D is also forty so these two are equal these two I call what are they vertically opposite angles so we can write they are equal example number one calculate the compliment of 38 what is complement means the sum is 90 degrees so complement angle is 90 minus 38 subtract you get 2 here and fast so 52 degrees is the complement angle if ABC is 48 PQR is 66 KLM is 42 and XYZ is 24 name the pairs of complementary angles among these angles so complimentary means 90 degrees find out what are the angles add up to 90 look at these two 48 plus 40 to 90 degree so you can say ABC and KL m complementary what is 66 and 24 at dancing 66 and 2490 so those are complementary so you can write P Q R and what's the other one 24 XYZ these also complementary angles example three explain whether the powers of angles given in the figure are supplementary angles so what's the condition for supplementary the angles add up to 180 so we'll check 62 plus 180 underneath so that means a OC + PQ are supplementary look at these 253 and 170 what's the sum 117 so not add up to 180 so you can write not supplementary angles exercise 3.1 copy and complete the complement of 60s but its complement of 60 90 minus 60 degrees supplementary of 60 180 minus 1620 the complement of 75 90 minus 75 so what's the anger 15 degrees supplement of 75 180 minus 75 now so hundred five degrees the complement of 25 is 90 minus 25 it's a 65 degrees supplement of 25 180 minus 25 hundred fifty-five degrees what's the complement of one degree 90 minus 189 degrees what is supplementary of one degrees that's hundred seventy-nine 180 minus one from among the angles ABC PQR KLM BOC mnl TEF select and write down two pairs of complementary angles and two pairs of supplementary angles so with first two complementary angles what are complementary add up to 90 degrees so we can take these two 72 and 80 90 degrees so BOC and ABC what is check 75 with 1575 and 1596 you are so those are complementary now we'll look at supplementary angles so hundred sixty-five and fifty what's the sum 165 and 1580 so supplementary means the angles add up to 180 so you can write k l m and p q r those are supplementary so what is 108 and 7280 so you get em in L angle + 108 and ABC ABC angle so these are supplementary angles question number three according to the figure given here what is the sum of B or C and C EOG first we'll find B or C vo C is 25 C OG C or D is given 65 so what's the sum add it together you get 10 and 9 so 90 degrees what is the complement of B or C so B or C and C or D are complementary angle so if it's B or C what's the other angle C or C what is the magnitude of a or G what is that a gee is this whole thing 20 plus 25 plus 65 what's the sum hundred tip what is the sum of a ood that's hundred ten and goe 70 so that's hundred eighty degrees what is the supplement of do e do en e yo D add up to 180 means those are supplementary angles so what's the supplement of D or e that's a or T what is the complement of do a D or E so do II what's a compliment 70 is there so 90 minus 70 that's 20 degrees now what is the anger so you need to find out a 20 degree angle that's complement of D or e so what's that 20 degree angle is a or b so you can write this is same as a oh yeah so that's the complement of do a 4 question right two pairs of complementary angles in the given figure complimentary means add up to 90 degrees so we can take this angle so two angles are there CD B angle plus or we can say plus B D anger it's 90 degrees the sum of two angles add up to 90 degrees so those are complementary angles what's the other one we can take here these two a b d angle and DB c angle that's add up to 90 degrees that's also complementary ax the straight line segments a b and c d intersect at oh right four pairs of supplementary angles in the figure supplementary means add up two hundred and eighty so look at that 80 plus hundred is 180 so i can write c oh a angle and a or d that's 180 because 80 and 100 that's supplementary then when you take other way rock a OD + d OB also 180 this way also supplementary now when you take C D line D OB angle + b OC angle that's also hundred eighty degrees and the last pair is when you take a beeline be your C angle and see o angle that's also hundred eighty degrees right two pairs of complementary angles according to the information marked in the given figure complementary means add up to 90 degrees so what are those yeah these 2 P X cube angle and q XR that's 90 degrees and also can you see that's why this is also 90 so we can write Q X R and R X that's also 90 degrees copy these statements in your exercise book and please tick in front of the correct statements and wrong mark in the front of the incorrect statements the complement of an acute angle is an acute angle 90 - a small angle so definitely it's an acute angle so this is correct the complement of an acute angle is an obtuse angle so cannot be more than 90 degrees because complement means 90 degrees so this is wrong the supplement an obtuse angle is an obtuse angle supplement means 180 so obtuse angle is in between 90 and 180 and it cannot be exceed 180 so that's wrong the supplement of an acute angle is an obtuse angle yes because if this is less than 90 180 minus that angle definitely you get an obtuse angle so the supplement of an acute angle is an obtuse angle that's correct example 1 explain whether the pairs of angles denoted by a B in the figures given below are pairs of adjacent angles so what are the conditions for adjacent angles there should be a common arm now look at this one okay Q are common and is there a fixed-point vertex point this is Q and this is r so no common vertex so these two are not adjacent angles so you need to check all three properties to satisfy four adjacent angles explain whether the pairs of angles denoted by a and B in the figures given below are pairs of adjacent angles yeah common vertex is there that's P is there a common arm here B P P see here a PN PD so no come on um so therefore a and B not adjacent angles example one explain whether the pairs of angles denoted by a B in the figures given below are pairs of adjacent angles so check B is this one and a is here here to here common vertex is o is there a common arm so these two are the lines and here this is the other line okay common arm you can take as Oh a now check whether these two angles on both sides of the way this is also measured this way this is also measured same way so these are not adjacent angles so you can write down measured angles on the same side of a common arm so therefore a and B are not budgets and angles example two in the given figure PR is a straight line segment find the magnitude of PQ s PQ s PQ R is a straight line so what is PQ s hundred eighty minus 45 because this is a straight angle and subtract 5 so this is 5 335 degrees example 3 find the magnitude of a or P so how we can find this is a straight line a B is a straight line so we can say this is a straight angle so what's the condition for a straight angle that's 180 so 2 X plus 3 X plus 50 degrees is equal to 180 because this is a straight angle 2x and 3x becomes 5x and take 50 to the other side subtract 50 from both sides you get 5x equals 180 minus 50 that's 130 so divide by 5 you get so X is equal to 5 times 2 10 for 30 that's 6 so 26 degrees exercise 3.2 write whether the pairs of angles marked as a and B in each figure is a pair of adjacent angles so what can you say about this Oh L is common Oh is the vertex point and this angle measured this way this is measured this way so angles on both sides so what can you say a and B are adjacent angles this one what's the common our vertex is okay so P is the vertex here we'll take this is the common ah Oh a not away P a is the common um let this angle measure this way this angle measured this way so on both sides so you can write a UH a and B measured both ways so that means a and B are adjacent triangles this diagram this is a and this is B here common arm is MX it means the fixed point that's vertex point but to this common arm this is measured same on the same side and be measured on the same side so not adjacent not adjacent angles if PQ is a straight line segments in each figure given below find the magnitude of the angle marked by an initiator so this is a straight line so what's x straight away you can write that's 180 minus 120 60 degrees what's the reason because of straight angle this one PQ is a straight line so what is a a is hundred eighty minus 68 because of straight angle 112 this one PQ is a straight line so what's T 180 minus 95 because of straight angle so 85 decrease when you look at this one how can we find out the X letter P Q is a straight line so you can write 40 plus 90 plus X is 180 40 plus 90 130 so what's X X is 180 minus hundred 30 that's equal to 50 degrees this one PQ is a straight line so we can write E Plus E Plus E is 180 so 3 a equals 180 equals 180 divided by 3 that's 60 degrees question number 3 in the figure if a B is a straight line segment find the magnitude of a og a og is 2x so a B is a straight line so what can you say about these three angles add up 280 because these three are on a straight line straight to X and X 3 X subtract 90 from both sides you get 3x is 180 minus 90 that's 90 degrees so how can we find out X divided by 3 you get 2x equals 30 degrees so what's a or D D is 2x so 2 times 30 60 degrees PQ is a straight line segment according to the information marked in the figure find the magnitude of P or s POS is 3x so we'll first find X we can see 3x plus 2x plus 80 is 180 degrees because of straight 3x and 2x becomes 5x subtract 80 from both sides you get 100 divided by 5 you get x value is 20 now you have X value what's the P or s Sanga P OS is 3x 3 times 20 that's 60 degrees and part two it says find the magnitude of s o Q so Q is 80 plus 2 times X 2 times 20 so according to Bodmin you have to do multiplication first 2 times 20 is 40 40 plus 80 120 degrees question number five conclude whether p oq' in each of the given figures is a straight line so we'll add NC 130 plus 50 you get 180 that means straight angle so Pete Oh Q or P or Q is a straight line this one we led 139 and 42 181 so that's not equal to 180 so you can write P or Q is not a straight line looks like it's straight but when you calculate the values it's not a straight line well I don't see this one 5588 37 180 so that means P or Q is a straight line this 145 plus 113 plus 22 that's also 180 so we can say P Oh Q is a straight example number one find the magnitude of the angle marked as a OD that's X in the given v so this is a point so we have to think about angles around the point so what's the sum of angles around the point that's 360 so what's 120 last 130 plus 90 you get here nine plus three twelve fourteen one remaining so three three hundred forty so we can write find X as 360 minus 340 because and girl around a point is 360 degrees so x equals 20 degrees example two APB is 150 DP see hundred so find B PC B P C is three X so we need to solve for X first so we know this is a fixed point and 150 and 101st you get 250 then we can write 2x plus 3x plus 250 is equal to 360 because angle around a point now solve 2x and 3x becomes 5x subtract 250 from both sides what you get you get 110 divided by 5 both sides you get x equals 5 times 2 10 5 times 2 10 so x equals 22 degree now we need to find out B PC anger so what's B PC angle is 3 X 3 times 22 you get 66 decrease exercise 3.3 find the value of x so this is a point so you can find the sum of all angles that's add up to 360 so first we will take 130 plus 160 you get 290 then X plus 290 is 360 around a point no subtract 290 from both sides you get what's the value 70 degrees for X find the value of a this is the point so we can say a plus 50 is 360 and go around a point so what's a subtract 50 from both sides you get 310 that's a reflex angle find the value of a so this is the point you can add all together a plus E Plus E Plus E is 360 for a equals 360 divide both sides by 4 you get a equals 90 degrees find the magnitude of APC APC is the whole angle so what's the value APC here this is also a PC this is also a PC so how you identify which one if it's a PC reflex angle this is this one more than 180 this is just the AP C angle so a PC angle is 360 minus these two value sum of these two values so 90 and 120 that's 210 so you subtract 210 from there so you get hundred 50 decrease so if it's a PC just the angle that can be obtuse angle a PC reflex means more than 180 degrees find the magnitude of SOR SOR is 3x so we'll first find X 110 plus 80 you get 190 then 2x and 3x plus 190 is 360 because this is angle around a point so 5x plus 190 is 360 subtract 190 from 360 what you get 16 so you get 7 and 1 so 5 sequels 170 divided by five thirty four degrees for X this is folks then how can we find out it's so our angle that's three x three x 34 three times 4 12 three times 3 9 plus one tip so hundred two degrees a B is a straight line if APR is 150 so this is given 150 find the magnitude of Q P B QP b is this angle so how we find out we can first find out these two angles and then subtract from this one you get the other angle now it's given a B is a straight line so what is this angle this angle this is 180 so I can write 150 plus x equals 180 because of straight angle and x equals subtract 150 you get 30 degrees for X now we found out X is this angle that's 30 now we need to find out this so what is B PQ or q PB angle is 180 minus 2x because this is also a straight angle now substitute 180 minus 2 times the t-bog mas according to bot mas multiplication first 180 minus 60 you get hundred twenty is the this angle QP be example number one find the magnitude of each angle around the point P in the given figure we are XY + KL a straight line segments so what can you say about this Sanga LP why angle is also 135 vertically opposite angles then what's this angle so this is a straight angle because L K is a straight line so you can write find x PL angle is 180 minus 135 that's straight angle 45 degrees that's x PL so x PL and KP y angles are vertically opposite angles so these two are equal so you can write that's 45 find the magnitude of each of the angles marked by an English letter in the figures given below ABCDEF a straight lines what are these two X is 43 vertically opposite angles we know that vertically opposite angles are equal this one what can you say about this one if you take this line and this line 130 is equal to this one so X plus 30 is 130 how can we find X subtract 30 from both sides that's equal to 100 degrees so here what's the reason vertically opposite angles okay these two are straight line what can you say about this and this a plus a is 135 vertically opposite angles are equal so 2a equals 135 divided by 2a inker 2 times 6 12 and 2 times 7 14 and one remaining means 67 point five degrees for a look at this one a B and C D are straight lines so this is equal to this one so we can write 90 plus 6 equals 125 so you can write down the razor vertically opposite angles subtract 90 from 125 to get X so you get 35 degrees this one what can you say about a B and C D yeah this angle is equal to this sang so what can you say straight to me B is 55 degrees vertically opposite angles then if you take the other two lines this one and this one this whole angle is equal to this whole angle so what can you say about 55 plus a is equal to 65 plus B B is 55 now add it together 120 so a equals subtract 55 from that you get 65 degrees for a now we found a and B what C see you can find out using straight angles so a plus B plus C is a straight line under an 80 what's a 65 what's B 55 now subtract these two angles you get the C well so what's the sum of these two 65 and 55 hundred-twenty so subtract 120 you get 60 degrees for C value so all of these angers we've found using vertically opposite angles here and this one straight angle find the values of the angles denoted by x y and z in the given figure b by BD x c are straight lines and ABC and AC b are a pair of complementary angles what is the magnitude of ABC first we'll find out XYZ here this and this vertically opposite angles so we can straight away write x equals 90 then Y is 58 same reason Z how can we find C C is 180 minus 58 because of straight angle subtraction 122 so Z is 122 so we found X Y C now they're asking to find out ABC but it's given ABC and ACB it says supplementary not supplemented complementary complementary means 90 degrees ABC you'll find out which angle ABC and AC B AC B angle that's why ACB is y so y plus ABC angle that's given 90 degrees we know the Y value so we can find out them ABC value 90 minus the Y value what's y 58 degrees subtract you get 32 degrees so because this is complementary so we covered all theory related to angles so we did the sum of pair of acute angles is 90 then we call these are complementary angles if the sum is equal to 180 that's supplementary angles an acute angle which needs to be added to a given acute angle for the sum of the two angles to be 90 is called a complementary and a pair of angles which have a common arc and a common vertex and are located on either side of the common arm is called pair of adjacent angles and the sum of angles located around a point on one side of a straight line is 180 and angles around up point is 360 and what's the other one we learned vertically opposite angles created by the intersection of two straight lines are equal to each other so practice all these exercises and examples and thorough with the angles listen

hello grade 8 children today I&#39;m here to teach you chapter 3 in your textbook that&#39;s angles this is a geometry lesson we&#39;ll see what are the basics related to angers what is an angle so angle is formed by two line segments from one center point so if we take this point oh oh a OB are the two lines so here we can say Oh a and OB pass from the center point oh oh is the vertex point we call this is the vertex point and it is fixed and Oh a and OB ah raise angle is what is the angle form we can write two ways we can start from a a OB so this is how we write a OB and we put a hatch above representing that o is the angle or we can start from the other side B or a so we can write like this or if it&#39;s one angle we can write down just a anger this is also possible so when you take this diagram you get two line segments and a fixed point so we can define angle as a rotation so how we can define an angle as a rotation rotation of a line segment what is the line if you take this one Oh a is the line segment around the point oh it&#39;s called the anger so when you rotate here to here you get an anger so this is the angle created and this is clockwise we are rotating clockwise from a units off angles what are the measurements we use we used degrees how we represent degrees so we put a small 0 so here superscript of 0 so if this is 30 degrees we put 30 and put a small 0 here so this means 30 degrees so you need tough measurement used for measuring and angle is decrease symbol for degrees is a small circle in the superscript so if you take the circle the entire circle so how many degrees is that so 360 so entire circle is recognized as 360 degrees so here can you see the degree sign 360 degrees starting angle at always zero because this is not rotating so here starting angle is zero degrees now we&#39;ll rotate half of a circle so this is the fixed line and starting from the fixed point or 1/4 of a circle we know the full circle is 360 so 360 and 1/4 of that what&#39;s the angle you&#39;ll get 90 degrees so this is 90 degrees normally we represent this angle as ur a square like this so that means this is 90 degrees then rotation of half of a circle so here to here is half of 360 so you get 180 degrees what about this one 3/4 so when you divide the circle into 4 parts this is starting from here 3/4 of a circle full circle is 360 3/4 of that 3/4 of 360 what&#39;s the value for x this 990 times 3 270 so this is 270 decrease so what are the types of angles that we need to learn so first one is acute angles what is that cute angle so the angle in between 0 and 90 degrees so less than 90 degrees and above 0 degrees is called acute angle right angle so right angle is 90 degrees so we represent using a square like this then obtuse means the angle is more than 90 degrees so here if this is 90 degrees this is more than 90 degrees and less than 180 degrees so we call it as obtuse angles what is straight angle means if the angle is 180 and this is a straight line so GFP is a straight line if it&#39;s a straight line we call this angle is a straight angle 180 degrees and you need to know another type of angle that&#39;s reflex angle reflex angle is angle above 180 so this is 180 line above 180 and below 360 so this is the 360 degree line so you can get either this type of angle oh yeah more than 270 also possible so this is up to here that&#39;s 270 so this angle is more than 270 as well so these two are called reflex angles or cheese and angles what are just and angles so angles e OB and b or c or c OB b or c adjacent angles in the above diagram so what are the properties in adjacent angles common arm is there so two these two angles this is the common arm one fixed line is there so that&#39;s Oh big you need to get a common vertex point so this is the vertex file so what&#39;s the vertex here Oh Oh vertex point and angle situated in opposite sides of the common so common arm is here so this sandal is anti-clockwise and this angle is clockwise so angle situated bow in both sides so these are the three properties satisfied for adjacent angles now identify in this diagram what are adjacent angles look at this o P lie when you take Opie line that&#39;s the common arm from here there&#39;s an anger anti-clockwise what&#39;s the angle P o our reflex angle P you are this is the reflex angle Modell&#39;s 180 and less than 360 and what&#39;s the other angle this is clockwise measured this angle P or Q so P or Q and P or our reflex angle ah adjacent angles with common arm o P so what&#39;s the fixed point here or is the vertex point look at this one identify what&#39;s the common arm and what are the two adjacent angles so when you look at this diagram we can see this is the common arm o our common arm and what are the two angles from this this is one q or r QR or you can write R Rho Q and what&#39;s the other one this one so we can write P or our reflex angle so these are the two adjacent angles in this diagram what&#39;s the common now we can see common arm is o Q and what are the two angles this one here measured anti-clockwise p or q p oq&#39; angle and what&#39;s the other angle Q or are these are adjacent angles with common arm or Q and what&#39;s the vertex point vertex point is o what are complementary angles two pairs of adjacent angles add up to 90 degrees we call those are complementary angle now take a look at these two this angle is 60 degrees and this is 30 degrees so what is 60 degree angle plus 30 degree angle you get 90 degree so the sum is 90 degree so we can say a Obi angle and P or a angle ah complementary angles because the sum of the two angles is equal to 90 degrees write down the complementary angle to the given angles thirty&#39;s there how you find out the other girl 90-30 that&#39;s 60 degrees 50 if one angle is 50 what&#39;s the other complementary angle you subtract 50 from 90 you get 40 degrees 85 90 minus 85 that&#39;s 5 degrees 24 90 minus 24 you get 66 degrees 36 90 minus 36 but you get you get 54 90 minus 36 and what about 3 degrees 90 minus 3 degrees you get 87 so these are complementary angles look at this one ninety degrees and zero are not complementary angles zero angle does not exist so don&#39;t take 90 and zero those are not complementary angles complementary adjacent angles so complementary means add up to 90 what are adjacent angles adjacent angles you need to have a fixed point vertex point comma Nam and the two angles to ated on both sides of the common Nam now look at this diagram you can see when you add a abd angle and DBC angle what&#39;s the sum this angle and this angle you can see is 90 degrees so that means these two angles are complementary now why this is complementary adjacent angles so when you take this diagram this is the common arm and this is the vertex point and this angle measured this way anti-clockwise this angle measured clockwise so the two angles on both sides of the common are so these are complementary adjacent angles supplementary adjacent angles supplementary means the sum of two angles add up to 180 now look at these two C B a or ABC and abd so what are the two angles 110 l70 so when you add it you&#39;re getting hundred eighty so we call two angles equal to 180 are supplementary angles and these are also adjacent when you take this common arm a B so when you take this slide on top of this line you&#39;re getting an angle like this so this is the BD lie so you can see Oh a is the common ah and this angle measured anti-clockwise this angle measured clockwise and this is the fixed point B so two angles equal to 180 are the supplementary angles and you can say a b c and a BD we are supplementary adjacent angles because when you take it together you get adjacent angles as well write down the supplementary angle to the given angles so what&#39;s the condition the sum is equal to 180 if 40 is the angle 180 minus 40 is the other supplementary angles that&#39;s 140 8500 80-85 mercy angle 5 and 1 remaining so that&#39;s 995 60 degrees 180 minus 60 that&#39;s 120 degrees 75 watts the supplementary angle 180 minus 75 you get Conrad 5 117 so subtract 117 from 180 63 degrees 29 you get all these are angles this is 29 so subtract you get one here and here subtract from 181 there and this is three so five 151 so these are the supplementary angles so what are supplementary angles the angle sum is 180 supplementary adjacent angles means we did that before so the sum is 180 as well as the two angles are adjacent now look at this guy Group abd is haunted DBC is 70° so when you add it you get 180 decrease so these are supplementary adjacent angles because when you take this is the common arm BD and the common vertex vertex is B and the two angles measured both sides those are the three properties for an adjacent angle now we look at what our vertically opposite angles now look at this one a B is a lie and C D is another line straight lines so intersect these two lines at O this is the intersection point so you get four angles there one two three four four angles and here&#39;s shaded once what are shaded ones e OC and the other one B OD a pair of vertically opposite angles so here this is one angle and this is the other vertically opposite angles now when you look at other way around this is also vertically opposite angle so what are the other unshaded Part A or D aug angle and be your C angle these are another pair of vertically opposite angles so how we get vertically opposite angles when you get any two straight lines intersecting each other now two lines are there pql SR so identify a pair of vertically opposite angles in the above diagram we can say this and this our vertically opposite angle so here P o R and s o Q angles are vertically opposite angles what are the other two this angle with this angle so you can write P o s angel&#39; and Q o our angle is also vertically opposite angles so you get two pairs of vertically opposite angles now one angle is given eighty degrees a OD anger so what&#39;s a or C angle we know C D is a straight line so what&#39;s the angle so if this is straight line this is a straight angle 180 so 180 minus 80 a OC angle is 100 a or D angle is 80 and also this is a straight line a B is a straight line so what&#39;s this angle this angle that&#39;s B or D angle B your J angle is also 180 so I can write a OD angle plus D B or D angle it&#39;s 180 so this is also 100 degrees so this is hundred that&#39;s B oh t angle so I can write B or D angle is hundred degrees now look at carefully this and this what can you say a oh D that&#39;s a or c a.o c and b or g angles we know that these are vertically opposite angles and also they are equal so remember the two vertically opposite angles now I can write a Oh C and B or D vertically opposite angles are equal similarly what can you say about the other one this is 80 this is also 80 so we found out this is also 80 so what&#39;s that B oh see anger so similarly I can write a OD and be your C angles are equal that&#39;s 80 degrees so we can say vertically opposite angles are equal this diagram identify vertically opposite angles that I equal POS POS is here what&#39;s the other vertically opposite angle this one Q or R if you take P or P o R naught P Q R this is P or R P o R is equal to this angle so that&#39;s Q or s so these two are vertically opposite angles find the values of a B and C what can you say about a angle can you see this is a straight line so a is 180 minus 100 because this is a straight angle so what&#39;s the answer eighty degrees then what you know about C angle E and C both are equal because those are vertically opposite angles so is 80 that means C is also 80 vertically opposite angles then what about B B and 100 these are two vertically opposite angles so we can say B is also 100 degrees because of vertically opposite angles this diagram find the values of P Q R this is 70 so this is a straight angle so what&#39;s be 180 minus 70 that&#39;s hundred check so we can write that&#39;s because of straight angle then you can write P is equal to R so this is hundred ten because of vertically opposite angles seventy and Q is also vertically opposite angles so Q is equal to 70 these two are because of vertically opposite angles now we look at angers around a point so the fixed point here is o so when you take from here around this point we know that the sum of angles add up to 360 degrees so here we can write all these angles so what are the angles X Y Z and this sandal is a all these angles add up to 360 degrees so when you get a point make sure that the sum of angles add up to 360 degrees find a and B so this is the fixed point so this is also around a point so how can we find out a now when you take this line this is a straight line this is 90 given here to here straight angle here to here straight angle because this is a straight line so what&#39;s a is 180 minus 90 degrees because this is given as 90 degrees so that&#39;s 90 but we know the angles around a point is 360 so what&#39;s big B is 360 minus all three angles so here what are the three angles 90 a is 90 and 100 so when you add it you get 280 degrees 280 degrees is the other three angles so what is B 360 minus 280 so what&#39;s the value 8 so B is 80 degrees look at this one this is a point so we can consider angles around a point to find out the value of a 60 plus 80 plus 80 what&#39;s the sum 220 and all the angles add up to 360 so what&#39;s a it is 360 minus 220 what&#39;s the answer answer is hundred forty degrees find the value of x here what can you say about this one this is a straight line so what&#39;s this angle straight angle so X plus X plus X is 180 because of straight angle then X plus X plus X is 3x is 180 divided by three you get the value of x so x equals 60 degrees you have given several angles and identify types of angles so acute means the angle less than 90 degrees 30 degrees is then an acute angle what are the other angles less than 90 55 68 84 forty-eight loser accurate right angle means 90-degree angle obtuse obtuse means more than 90 less than hundred eighty degrees hundred twenty hundred forty 170 hundred twelve what is less than hundred eighty visa more than 180 straight angle means equals two hundred and eighty so I can take 180 degree n then what are reflex angles reflex angles are more than 180 and less than 360 so 270 195 200 and 318 those are the reflex angles you have given several angles and you are asked to write down pair of complementary angles complementary means the sum add up to 90 degrees what are the angles add up to 90 degrees look at 70 and 20 at up to 90 degrees so you can write a b c and k l so these are complementary angles add up to 90 degrees and write down the pair of supplementary angles what are supplementary means add up to 180 this sand that&#39;s 150 plus 30 you get 180 so x y z and c d e are supplementary angles because these are add up 280 identify the type of angles so what is this angle less than 90 degrees acute angle this one more than 90 degrees obtuse this one also less than 90 degrees acute and we look at some more angles this is more than 90 degrees less than 180 no twos angle this one yeah 90 degrees so what you call for 90 degrees right angle this one 180 straight angle this one more than 180 what you call that reflex this is also more than 180 so that&#39;s also reflex this is 90 degrees so what is 90 means right angle this is two straight lines intersect at one point so what are these two vertically opposite angles find X in this diagram we know this is a straight line and this is add up to 180 so 2x plus X plus 60 is hundred eighty now take 60 to the other side that means subtract first we&#39;ll add these two to X and X becomes 3x and subtract 60 from both sides you get 3x equals 180 minus 60 degrees left 180 minus 60 means 123 X 620 means divide this by 3 you get x equals 40 degrees I&#39;m glad 20 divided by 3 so X is 40 degrees find X in this diagram this is mentioned this is 90 degrees so 2x plus x equals 90 degrees what are those complementary 2 X plus X is 3x equals 90 degrees divide this by 3 you get x equals 30 90 divided by 3 find ABC can you see this one and this one vertically opposite angle so a equals 85 you can write down what the reason vertically opposite angles then B equals what when you take this straight line B equals 180 minus 85 so B equals 180 minus 85 because of straight angle so subtract you get 5 and 9 so 95 is the B value now what is C B and C are vertically opposite angles so we can say see also 95 because of vertically opposite angles a bee is a straight line find ABC so I&#39;ll put a bee here a bee is a straight line fine ABC now when you take this three angles a plus 3a plus two ways hundred eighty that&#39;s a straight angle so add it together 3 + 2 5 + 1 this becomes 6 8 equals 180 when you divide by 6 you can get there a value so you get a equals 30 degrees now we&#39;ll look at this one this side lower side here what can you say about 4 a and B that&#39;s also straight angles so before that we&#39;ll find out for a is 34 times 30 is 4 that&#39;s 120 degrees now what can you say about these two angles these are straight angles so for a and B straight angles so 180 minus 4 is equal to B so you can&#39;t just subtract 180 minus 120 that&#39;s 60 degrees because these two are straight angles look at this one find y when x equals hundred check so this is given hundred and ten what&#39;s the Y value we know this is straight line so Y is hundred eighty minus hundred check so that&#39;s 70 degrees find y when x equals 150 if this is 150 what&#39;s the relationship 180 minus 150 is why so that becomes thirty and then here find X when y equals forty same thing happens X is equal to again 180 minus the Y value now why is for T you get hundred forty degrees find X when y equals fifty these two are straight angles so you can subtract from 180 so you get 130 there this one this is a fixed point what&#39;s 50 and 30 and you shown is 80 this is 80 80 plus two x two x three X is equal to write it here these three angles add up to two x two x three exist have an X and this is equal to what is this 180 degrees so all together is 7x and this is 50 and 30 80 all together what&#39;s equal to this is equal to hundred eighty or 360 this is a point 360 degrees so angle at a point angle around a point so what is 7x 360 minus 80 degrees so you can subtract you get 280 so 7x equals 280 so what&#39;s what&#39;s the value divided by 7 to get the x value so X is equal to 40 degrees so make sure this is a point so angle sum of a point is 360 look at this one it&#39;s given a OD AOC b OC the sum is 260 find the values of all four angles so what&#39;s this Stanga BOJ angle so b OD angle is 360 it&#39;s minus 260 because this is a point and sum of angles around a point is 360 so 360 minus 260 you get hundred decrease that&#39;s for B or D then what can you say B or D angle and this angle AOC angle both are equal vertically opposite angles so you can write a OC is equal to 100 degrees so this is hundred this is hundred then how can you find out be your C anger we know a B is a straight line this is 100 so this becomes 180 minus 100 that&#39;s 80 degrees now Bo say is 80 means a OD is also 80 degrees that&#39;s vertically opposite angles look at this one a B and C D are straight lines intersect at oh this is a fixed point find the value of x what can you say about this angle and this angle these two are equal vertically opposite angles so X and X 2x is equal to 80 degrees so how we find out X divide by 2 so X is equal to 40 degrees find a from this diagram we can first add 60 and 40 is 100 hundred degrees so for a is what this is a straight angle so for a equals 180 minus 100 that&#39;s 80 degrees so how you find out a divided by 4 so a equals 20 degrees look at this diagram and find out what&#39;s the value of a this is a point so we can add all these angles add up to 360 so 5 + 2 7 7 + 3 10 10 plus 2 12 a is 360 so what&#39;s a divided by a equals 30 decrease find X here this is a straight angle X plus 30 plus X plus 20 and 60 and up to 180 now I&#39;d like terms x + X becomes 2 X 30 plus 20 50 50 plus 60 hundred ten now how we find out X so 2x equals subtract 180 from subtract 110 from 180 you get 70 degrees is 2x divide by 2 what you get X is equal to 35 70 divided by 2 is 35 find ABC PQR all these angles this is a straight angle so a is 180 minus 70 so hundred check what&#39;s B P is 70 because this and this both are vertically opposite angles B is 70 vertically opposite angles see a and C vertically opposite angles so C is equal to 110 that&#39;s vertical same reason this side this is also another point two straight lines are there so straight away you can write P equals 180 minus 150 that&#39;s 30 degrees because of straight angle then q q 150 both are vertically opposite angles so Q is 150 vertically opposite angles and what&#39;s our R and P both are equal those are vertically opposite angles so our a same as P that&#39;s 30 degrees the reason is the same vertically opposite angles a B and C D are straight lines find ABC this is 90 degrees so what&#39;s 90 plus 60 on Brad 50 so what&#39;s a because this is a straight angle a is 180 minus 150 that&#39;s 30 degrees so what&#39;s the reason straight angle what&#39;s the B value we is 60 degrees what&#39;s the reason vertically opposite angles then let&#39;s see what can you say about si si is these two lines so this and this a with 90 vota vertically opposite angles so a plus 90 so 90 plus 30 you get 120 vertically opposite angles now we will look at the review exercise so we covered about obtuse acute reflex angles and complementary and what is supplementary angles and vertically opposite angles so now we will see how we can apply those properties in the exercises look at the first question copy the two groups a and B given below and join them appropriately 135 which type of angle it says obtuse angle 90 is right angle 180 is a straight angle 35 is acute angle 245 is reflex angle more than 180 and 990 also reflex angle and 280 also reflex angles by considering the given figure find the magnitude of each of the angles given below and cried the type of each angle a OB a OB is 90 degrees what&#39;s the anchor right angle C or D C OD given that that&#39;s 40 degrees that&#39;s a acute angle B OD which one is B OD b o T that&#39;s also 90 degrees that&#39;s a right angle and B or C this angle so how can we find out vo C 90 minus 40 90 minus 40 is 50 degrees so that&#39;s an acute angle AOC 90 Plus this so this is 50 we found so a oh C is equal to 90 plus 50 so what is ninety plus fifteen hundred forty degrees a OD so a OD is a straight line so 180 that&#39;s straight angle look at this one draw the following angles using a protractor and name them so first one is PQ R so what we do we take the ruler and draw a straight line okay and then what we do we take a point P we take the point Q because you have to draw the angle PQR now take the protractor what we do we keep it on top of the point Q and measure the angle so what&#39;s the angle sixty degrees from here anti-clockwise we can mark the point so this is the point here 60 degrees so you can move this and draw the line passes through this point and this point so I can draw the line like this so that&#39;s P QR 60 degree angle so this is 60 degrees now look at this one ABC is 90 degrees so how we draw the 90 degree angle draw a line and then you can mark the angle here B angle so we&#39;ll take any point B now we can measure 90 degrees so take the ruler not the ruler protractor and keep the protractor on top of point B and Misha here you have to keep it properly this one on top of this line so something like this yes still not okay so here make sure that you keep them okay so here now it&#39;s correct so keep on top of the line now mark the point 90 degrees from here so this is the mark and you can draw the line now take the ruler connect this point and this point that&#39;s 90 degree and so this is 90 degree angle so you need to label this this is a B C so ABC is 90 degrees 130 degrees so what you do take a line and draw the line there and you need to mark a point so we&#39;ll take this point is there this so why now we need to measure 130 degrees so take the protractor keep on top of the line and here on this point zero point on Y now from here you have to measure that&#39;s hundred thirty so here to here this is 130 mark take the projector away and now you can take the ruler and connect this point with this one then what&#39;s the angle XYZ so we can mark this is X Y Z and this is 130 degrees this way is 130 degrees 48 degrees so how we draw 48 so take the ruler and then Mark a point will mark L so this is the point we have to mark that&#39;s angle then 48 degrees take the protractor keep on top of this and mark 48 degrees so 48 is here 40 and in between 50 and here so this is 48 now you can connect these two points with a ruler so mark it and then connect label the two points K and K L M angle is 48 degrees question number four as shown in the figure draw two straight line segments a B and C D such that they intersect each other at Oh make sure the magnitude of each of the angles AOC that&#39;s this angle C or B this one and B or G this one and a or D so all four angles we need to mission and write them down what is the value of AOC and c OB with first measured using the protractor take the protractor keep on top of this line and you can measure this part so here in your protractor you can measure from this way as well my one you only from this side so I have to subtract this value from 180 so 180 minus 140 so here to here is 40 degrees so I can write a or C angle is 40 degrees then boc angle or c OB angle i can measure from here that&#39;s 144 you you can measure from both sides zero is here as well as zero is here so look at carefully and measure the correct way so c OB is an obtuse angle that&#39;s hundred forty now a OC with measured co b b OD so how do you do B or D B or D is this way so we need to keep the protractor this way so this way and we can measure here to here that&#39;s 40 degrees b OD is 40 degrees here to here you can measure so 180 minus 40 or i can get straight away hundred forty-four a OD angle a OG is hundred forty degrees now what is the value of AOC plus Co be these two AOC is 40 degrees C or B is 140 so when you add these two what you get hundred eighty degrees so those two are 180 degrees are the two angles AOC and b OD equal to each other AOC forty B or D is also forty so these two are equal these two I call what are they vertically opposite angles so we can write they are equal example number one calculate the compliment of 38 what is complement means the sum is 90 degrees so complement angle is 90 minus 38 subtract you get 2 here and fast so 52 degrees is the complement angle if ABC is 48 PQR is 66 KLM is 42 and XYZ is 24 name the pairs of complementary angles among these angles so complimentary means 90 degrees find out what are the angles add up to 90 look at these two 48 plus 40 to 90 degree so you can say ABC and KL m complementary what is 66 and 24 at dancing 66 and 2490 so those are complementary so you can write P Q R and what&#39;s the other one 24 XYZ these also complementary angles example three explain whether the powers of angles given in the figure are supplementary angles so what&#39;s the condition for supplementary the angles add up to 180 so we&#39;ll check 62 plus 180 underneath so that means a OC + PQ are supplementary look at these 253 and 170 what&#39;s the sum 117 so not add up to 180 so you can write not supplementary angles exercise 3.1 copy and complete the complement of 60s but its complement of 60 90 minus 60 degrees supplementary of 60 180 minus 1620 the complement of 75 90 minus 75 so what&#39;s the anger 15 degrees supplement of 75 180 minus 75 now so hundred five degrees the complement of 25 is 90 minus 25 it&#39;s a 65 degrees supplement of 25 180 minus 25 hundred fifty-five degrees what&#39;s the complement of one degree 90 minus 189 degrees what is supplementary of one degrees that&#39;s hundred seventy-nine 180 minus one from among the angles ABC PQR KLM BOC mnl TEF select and write down two pairs of complementary angles and two pairs of supplementary angles so with first two complementary angles what are complementary add up to 90 degrees so we can take these two 72 and 80 90 degrees so BOC and ABC what is check 75 with 1575 and 1596 you are so those are complementary now we&#39;ll look at supplementary angles so hundred sixty-five and fifty what&#39;s the sum 165 and 1580 so supplementary means the angles add up to 180 so you can write k l m and p q r those are supplementary so what is 108 and 7280 so you get em in L angle + 108 and ABC ABC angle so these are supplementary angles question number three according to the figure given here what is the sum of B or C and C EOG first we&#39;ll find B or C vo C is 25 C OG C or D is given 65 so what&#39;s the sum add it together you get 10 and 9 so 90 degrees what is the complement of B or C so B or C and C or D are complementary angle so if it&#39;s B or C what&#39;s the other angle C or C what is the magnitude of a or G what is that a gee is this whole thing 20 plus 25 plus 65 what&#39;s the sum hundred tip what is the sum of a ood that&#39;s hundred ten and goe 70 so that&#39;s hundred eighty degrees what is the supplement of do e do en e yo D add up to 180 means those are supplementary angles so what&#39;s the supplement of D or e that&#39;s a or T what is the complement of do a D or E so do II what&#39;s a compliment 70 is there so 90 minus 70 that&#39;s 20 degrees now what is the anger so you need to find out a 20 degree angle that&#39;s complement of D or e so what&#39;s that 20 degree angle is a or b so you can write this is same as a oh yeah so that&#39;s the complement of do a 4 question right two pairs of complementary angles in the given figure complimentary means add up to 90 degrees so we can take this angle so two angles are there CD B angle plus or we can say plus B D anger it&#39;s 90 degrees the sum of two angles add up to 90 degrees so those are complementary angles what&#39;s the other one we can take here these two a b d angle and DB c angle that&#39;s add up to 90 degrees that&#39;s also complementary ax the straight line segments a b and c d intersect at oh right four pairs of supplementary angles in the figure supplementary means add up two hundred and eighty so look at that 80 plus hundred is 180 so i can write c oh a angle and a or d that&#39;s 180 because 80 and 100 that&#39;s supplementary then when you take other way rock a OD + d OB also 180 this way also supplementary now when you take C D line D OB angle + b OC angle that&#39;s also hundred eighty degrees and the last pair is when you take a beeline be your C angle and see o angle that&#39;s also hundred eighty degrees right two pairs of complementary angles according to the information marked in the given figure complementary means add up to 90 degrees so what are those yeah these 2 P X cube angle and q XR that&#39;s 90 degrees and also can you see that&#39;s why this is also 90 so we can write Q X R and R X that&#39;s also 90 degrees copy these statements in your exercise book and please tick in front of the correct statements and wrong mark in the front of the incorrect statements the complement of an acute angle is an acute angle 90 - a small angle so definitely it&#39;s an acute angle so this is correct the complement of an acute angle is an obtuse angle so cannot be more than 90 degrees because complement means 90 degrees so this is wrong the supplement an obtuse angle is an obtuse angle supplement means 180 so obtuse angle is in between 90 and 180 and it cannot be exceed 180 so that&#39;s wrong the supplement of an acute angle is an obtuse angle yes because if this is less than 90 180 minus that angle definitely you get an obtuse angle so the supplement of an acute angle is an obtuse angle that&#39;s correct example 1 explain whether the pairs of angles denoted by a B in the figures given below are pairs of adjacent angles so what are the conditions for adjacent angles there should be a common arm now look at this one okay Q are common and is there a fixed-point vertex point this is Q and this is r so no common vertex so these two are not adjacent angles so you need to check all three properties to satisfy four adjacent angles explain whether the pairs of angles denoted by a and B in the figures given below are pairs of adjacent angles yeah common vertex is there that&#39;s P is there a common arm here B P P see here a PN PD so no come on um so therefore a and B not adjacent angles example one explain whether the pairs of angles denoted by a B in the figures given below are pairs of adjacent angles so check B is this one and a is here here to here common vertex is o is there a common arm so these two are the lines and here this is the other line okay common arm you can take as Oh a now check whether these two angles on both sides of the way this is also measured this way this is also measured same way so these are not adjacent angles so you can write down measured angles on the same side of a common arm so therefore a and B are not budgets and angles example two in the given figure PR is a straight line segment find the magnitude of PQ s PQ s PQ R is a straight line so what is PQ s hundred eighty minus 45 because this is a straight angle and subtract 5 so this is 5 335 degrees example 3 find the magnitude of a or P so how we can find this is a straight line a B is a straight line so we can say this is a straight angle so what&#39;s the condition for a straight angle that&#39;s 180 so 2 X plus 3 X plus 50 degrees is equal to 180 because this is a straight angle 2x and 3x becomes 5x and take 50 to the other side subtract 50 from both sides you get 5x equals 180 minus 50 that&#39;s 130 so divide by 5 you get so X is equal to 5 times 2 10 for 30 that&#39;s 6 so 26 degrees exercise 3.2 write whether the pairs of angles marked as a and B in each figure is a pair of adjacent angles so what can you say about this Oh L is common Oh is the vertex point and this angle measured this way this is measured this way so angles on both sides so what can you say a and B are adjacent angles this one what&#39;s the common our vertex is okay so P is the vertex here we&#39;ll take this is the common ah Oh a not away P a is the common um let this angle measure this way this angle measured this way so on both sides so you can write a UH a and B measured both ways so that means a and B are adjacent triangles this diagram this is a and this is B here common arm is MX it means the fixed point that&#39;s vertex point but to this common arm this is measured same on the same side and be measured on the same side so not adjacent not adjacent angles if PQ is a straight line segments in each figure given below find the magnitude of the angle marked by an initiator so this is a straight line so what&#39;s x straight away you can write that&#39;s 180 minus 120 60 degrees what&#39;s the reason because of straight angle this one PQ is a straight line so what is a a is hundred eighty minus 68 because of straight angle 112 this one PQ is a straight line so what&#39;s T 180 minus 95 because of straight angle so 85 decrease when you look at this one how can we find out the X letter P Q is a straight line so you can write 40 plus 90 plus X is 180 40 plus 90 130 so what&#39;s X X is 180 minus hundred 30 that&#39;s equal to 50 degrees this one PQ is a straight line so we can write E Plus E Plus E is 180 so 3 a equals 180 equals 180 divided by 3 that&#39;s 60 degrees question number 3 in the figure if a B is a straight line segment find the magnitude of a og a og is 2x so a B is a straight line so what can you say about these three angles add up 280 because these three are on a straight line straight to X and X 3 X subtract 90 from both sides you get 3x is 180 minus 90 that&#39;s 90 degrees so how can we find out X divided by 3 you get 2x equals 30 degrees so what&#39;s a or D D is 2x so 2 times 30 60 degrees PQ is a straight line segment according to the information marked in the figure find the magnitude of P or s POS is 3x so we&#39;ll first find X we can see 3x plus 2x plus 80 is 180 degrees because of straight 3x and 2x becomes 5x subtract 80 from both sides you get 100 divided by 5 you get x value is 20 now you have X value what&#39;s the P or s Sanga P OS is 3x 3 times 20 that&#39;s 60 degrees and part two it says find the magnitude of s o Q so Q is 80 plus 2 times X 2 times 20 so according to Bodmin you have to do multiplication first 2 times 20 is 40 40 plus 80 120 degrees question number five conclude whether p oq&#39; in each of the given figures is a straight line so we&#39;ll add NC 130 plus 50 you get 180 that means straight angle so Pete Oh Q or P or Q is a straight line this one we led 139 and 42 181 so that&#39;s not equal to 180 so you can write P or Q is not a straight line looks like it&#39;s straight but when you calculate the values it&#39;s not a straight line well I don&#39;t see this one 5588 37 180 so that means P or Q is a straight line this 145 plus 113 plus 22 that&#39;s also 180 so we can say P Oh Q is a straight example number one find the magnitude of the angle marked as a OD that&#39;s X in the given v so this is a point so we have to think about angles around the point so what&#39;s the sum of angles around the point that&#39;s 360 so what&#39;s 120 last 130 plus 90 you get here nine plus three twelve fourteen one remaining so three three hundred forty so we can write find X as 360 minus 340 because and girl around a point is 360 degrees so x equals 20 degrees example two APB is 150 DP see hundred so find B PC B P C is three X so we need to solve for X first so we know this is a fixed point and 150 and 101st you get 250 then we can write 2x plus 3x plus 250 is equal to 360 because angle around a point now solve 2x and 3x becomes 5x subtract 250 from both sides what you get you get 110 divided by 5 both sides you get x equals 5 times 2 10 5 times 2 10 so x equals 22 degree now we need to find out B PC anger so what&#39;s B PC angle is 3 X 3 times 22 you get 66 decrease exercise 3.3 find the value of x so this is a point so you can find the sum of all angles that&#39;s add up to 360 so first we will take 130 plus 160 you get 290 then X plus 290 is 360 around a point no subtract 290 from both sides you get what&#39;s the value 70 degrees for X find the value of a this is the point so we can say a plus 50 is 360 and go around a point so what&#39;s a subtract 50 from both sides you get 310 that&#39;s a reflex angle find the value of a so this is the point you can add all together a plus E Plus E Plus E is 360 for a equals 360 divide both sides by 4 you get a equals 90 degrees find the magnitude of APC APC is the whole angle so what&#39;s the value APC here this is also a PC this is also a PC so how you identify which one if it&#39;s a PC reflex angle this is this one more than 180 this is just the AP C angle so a PC angle is 360 minus these two value sum of these two values so 90 and 120 that&#39;s 210 so you subtract 210 from there so you get hundred 50 decrease so if it&#39;s a PC just the angle that can be obtuse angle a PC reflex means more than 180 degrees find the magnitude of SOR SOR is 3x so we&#39;ll first find X 110 plus 80 you get 190 then 2x and 3x plus 190 is 360 because this is angle around a point so 5x plus 190 is 360 subtract 190 from 360 what you get 16 so you get 7 and 1 so 5 sequels 170 divided by five thirty four degrees for X this is folks then how can we find out it&#39;s so our angle that&#39;s three x three x 34 three times 4 12 three times 3 9 plus one tip so hundred two degrees a B is a straight line if APR is 150 so this is given 150 find the magnitude of Q P B QP b is this angle so how we find out we can first find out these two angles and then subtract from this one you get the other angle now it&#39;s given a B is a straight line so what is this angle this angle this is 180 so I can write 150 plus x equals 180 because of straight angle and x equals subtract 150 you get 30 degrees for X now we found out X is this angle that&#39;s 30 now we need to find out this so what is B PQ or q PB angle is 180 minus 2x because this is also a straight angle now substitute 180 minus 2 times the t-bog mas according to bot mas multiplication first 180 minus 60 you get hundred twenty is the this angle QP be example number one find the magnitude of each angle around the point P in the given figure we are XY + KL a straight line segments so what can you say about this Sanga LP why angle is also 135 vertically opposite angles then what&#39;s this angle so this is a straight angle because L K is a straight line so you can write find x PL angle is 180 minus 135 that&#39;s straight angle 45 degrees that&#39;s x PL so x PL and KP y angles are vertically opposite angles so these two are equal so you can write that&#39;s 45 find the magnitude of each of the angles marked by an English letter in the figures given below ABCDEF a straight lines what are these two X is 43 vertically opposite angles we know that vertically opposite angles are equal this one what can you say about this one if you take this line and this line 130 is equal to this one so X plus 30 is 130 how can we find X subtract 30 from both sides that&#39;s equal to 100 degrees so here what&#39;s the reason vertically opposite angles okay these two are straight line what can you say about this and this a plus a is 135 vertically opposite angles are equal so 2a equals 135 divided by 2a inker 2 times 6 12 and 2 times 7 14 and one remaining means 67 point five degrees for a look at this one a B and C D are straight lines so this is equal to this one so we can write 90 plus 6 equals 125 so you can write down the razor vertically opposite angles subtract 90 from 125 to get X so you get 35 degrees this one what can you say about a B and C D yeah this angle is equal to this sang so what can you say straight to me B is 55 degrees vertically opposite angles then if you take the other two lines this one and this one this whole angle is equal to this whole angle so what can you say about 55 plus a is equal to 65 plus B B is 55 now add it together 120 so a equals subtract 55 from that you get 65 degrees for a now we found a and B what C see you can find out using straight angles so a plus B plus C is a straight line under an 80 what&#39;s a 65 what&#39;s B 55 now subtract these two angles you get the C well so what&#39;s the sum of these two 65 and 55 hundred-twenty so subtract 120 you get 60 degrees for C value so all of these angers we&#39;ve found using vertically opposite angles here and this one straight angle find the values of the angles denoted by x y and z in the given figure b by BD x c are straight lines and ABC and AC b are a pair of complementary angles what is the magnitude of ABC first we&#39;ll find out XYZ here this and this vertically opposite angles so we can straight away write x equals 90 then Y is 58 same reason Z how can we find C C is 180 minus 58 because of straight angle subtraction 122 so Z is 122 so we found X Y C now they&#39;re asking to find out ABC but it&#39;s given ABC and ACB it says supplementary not supplemented complementary complementary means 90 degrees ABC you&#39;ll find out which angle ABC and AC B AC B angle that&#39;s why ACB is y so y plus ABC angle that&#39;s given 90 degrees we know the Y value so we can find out them ABC value 90 minus the Y value what&#39;s y 58 degrees subtract you get 32 degrees so because this is complementary so we covered all theory related to angles so we did the sum of pair of acute angles is 90 then we call these are complementary angles if the sum is equal to 180 that&#39;s supplementary angles an acute angle which needs to be added to a given acute angle for the sum of the two angles to be 90 is called a complementary and a pair of angles which have a common arc and a common vertex and are located on either side of the common arm is called pair of adjacent angles and the sum of angles located around a point on one side of a straight line is 180 and angles around up point is 360 and what&#39;s the other one we learned vertically opposite angles created by the intersection of two straight lines are equal to each other so practice all these exercises and examples and thorough with the angles listen

Transcript for:Chapter 3: Angles

Transcript for:
Chapter 3: Angles