∴ x + y = 85° + 50° = 135°, Question 41. ⇒ ∠PQU = 35° ———- (i) ⇒ 130° = b (a) one of its angles is acute? 90°, Question 55. Solution: ⇒ ∠Q = 180° – 60° = 120°, Question 13. \(\Rightarrow \quad x=\frac{200^{\circ}}{2}=100^{\circ}\) Since, l || m and p is a transversal. ∴ a + b = c [Alternate interior angles], Question 106. Solution: Solution: (c) Estimate atleast two situations such that the angles formed by different positions of two players are complement to each other. Angles which are both supplementary and vertically opposite are False. (d) 64° (c) both are acute (b) how many types of angles are formed? When two angles together are equal to a straight angle -- to two right angles -- we say that they are supplements of one another, or that they are supplementary angles. ∴ ∠1 = ∠2 [Alternate interior angles] As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary True ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] According to question, Question 72. (c) Since, angles are on a straight line. ∴ x + y = 90° ———(i) [Angles are complementary] True, Question 64. (b) (iii) is false Now, p || q and m is a transversal. Solution: ∠1 +∠2 = 180° [Angles on a straight line PQ] In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If two supplementary angles are in the ratio 1 : 2, then the bigger angle is ⇒ 5b – 180° – 80° = 100° ∴ x + 64° + 46° +100° – 360° Solution: ⇒ x = 180° – 66° = 114° Question 30. Adding (i) and (ii), we get ∴ Its supplement = 180° – x Now, l || m and p is a transversal. According to question, (iv) c and f (b) If one of the angles is obtuse, then other angle of a linear pair is acute. ∴ a = 20° [Alternate interior angles] (c) 79° Solution: Given that. If they travel a distance of 5000 km during the entire journey and during the jo (c) 90° Then, which one of the following is not true? ⇒ (3a – b)° = 180° – (2a + b)° ∴ ∠POQ + ∠QOR = 180° [Linear pair] ⇒ 720° = 5x (b) 60° Two angles are “equal and supplementary” to each other. \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. As two right angles are supplementary to each other. ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. (c) 5° Solution: (c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles. As per the Congruent supplement Theorem, two angles which are are supplementary to the same angles then those two sets of angles are congruent to each other. An angle is more than 45°. Question 67. 3.Two angles that are congruent are sometimes right. \(\Rightarrow \quad b=\frac{120^{\circ}}{3}=40^{\circ}\) (d) making a linear pair (a) Since, PQ || RS and RQ is a transversal (d) 10° ⇒ ∠2 = 180° – 42° – 68° [Using (i)] \(\Rightarrow \quad x=\frac{180^{\circ}}{4}=45^{\circ}\) ⇒ 5b + 2 × 40° = 180° (ii) Name all the pairs of complementary angles. Draw a histogram (c) Draw a line L.M passing through T such that LM || QP || SR. (iii) uncommon arms are always opposite rays. Both angles of a pair of supplementary angles can never be acute angles. According to question, Solution: The value of bis NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. We have, Two perpendicular lines form two pair of supplementary vertical angles. If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is So, this player has the best kicking angle. Linear, Question 51. (a) ∠TOS and ∠SQR is a pair of complementary angles. The legs of a stool make an angle of 35″ with the floor as shown in figure. A linear pair may have two acute angles. Now, LM || QP and QT is a transversal. (c) 13° Solution: (a) 30° \(\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}\) ⇒ 50° + ∠BCD = 180° ⇒ ∠3 – 180° – 105° = 75° [From (ii) part] In the given figure, the value of y is Can two angles be supplementary, if both of them be right? (a) interior angles on the same side of the transversal Vertically opposite angles are either both acute angles or both obtuse angles. Now, PQ || RT and RQ is a transversal. Question 89. Two angles are said to be complementary to each other if their sum equals to 90° (right angle). (i) EF and GH Two angles forming a _________ pair are supplementary. Those Adjacent Angles Are Complementary. \(\Rightarrow x=\frac{300^{\circ}}{3}=100^{\circ}\) (a) 29° (a) complementary What is the type of other angle of a linear pair if Both angles of a pair of supplementary angles can never be acute angles. ⇒ 5a + 130° = 180° ⇒ a = 180° – 100° = 80°. ∴ a = 65° [Alternate interior angles] ⇒ x = 360°- 210° 7 Answers. (d) supplementary ChewBar. (c) 64° Solution: According to question, ∴ 4c = 120° [Corresponding angles] EASY. In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. (a) 110° ∴ Other angle is 180° – x. Adding (i) and (ii), we get ∴ b + 132° = 180° [Co-interior angles] (i) Yes, and b are the adjacent angles as they have a common vertex, one common arm and other non-common arms on the opposite side of the common arm. Now, SOT is a straight line If /_A<90^o and /_B<90^o then /_A+/_B < 180^o Therefore, two acute angle cannot be supplementary to each other. ∴ b + d = 180° [Co-interior angles] When two angles add to 90°, we say they "Complement" each other. (d) 150° Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. Answered By . We can see this if we start at the top left and work our way clockwise around the figure: (∵ 45° + 45° = 90° and 60° + 30°= 90°). 8. In the given figure, PO || RT. ∴ ∠COF = ∠EOD = 110° [Using (i)] [Vertically opposite angles] ⇒ 130° + y = 180° (b) ∠2 + ∠5 =180° Solution: In the given figure, AB||CD. Question 5. Supplementary angles are two angles whose measures sum to 180 degrees. ∴ 4c = 3b [Corresponding angles] (a) 35° (d) 30° ∴ a = f [Corresponding angles] We can see this because they are always supplementary with the same angle. two angles that have a common side are____ adjacent. False ∴ a = 132 [Corresponding angles] Solution: While vertical angles are not always supplementary, adjacent angles are always supplementary. (ii) ∠PQT and ∠PQR; ∠ORU and ∠QRP; ∠RPS and ∠RPQ are adjacent angles. Since, l || m and q is a transversal. (i) Name all the pairs of adjacent angles. Also, AB || DF and BD is a transversal. \(\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}\) Obtuse, Question 52. ∴ Angles between South and West and South and East are making a linear pair. \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. Solution: - 32510872 In the given figure, the value of x is (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. Solution: \(\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}\) ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] (d) equal ⇒ 3x = 180° Solution: (b) Since, POQ is a straight line always. Solution: ⇒ ∠2 = ∠y = 120° [Vertically opposite angles] Thus, one angle is 44° and other is 46°. (d) (ii) is false Vertical Angles: When two lines crosses or intersects each other, the angles are said to be vertical angles. In the given figure, P, Q and R are collinear points and TQ ⊥ PR, ⇒ 5a = 180° + 20° = 200° We have, ⇒ ∠y = 180° – 35° = 145° (b) 90°, 90° (d) 119° My answer-- Vertical angles As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary. the legs of an isosceles triangle are equal. Explain your answer. (b) 135° ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] Or does the complementary rule only apply to two angles? The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. ∴ x = 85° [Altemate interior angles] A + B = 90° (a) ∠1 = ∠3 Give reason. Solution: (a) Since, POR is a straight line. a = ∠1 + ∠2 = 60° + 30° = 90°. In the given figure, PQ||RS and a : b = 3 : 2. Solution: For given figure, statements p and q are given below: Now, RS is a straight line. ∴ ∠AOE + ∠EOD + ∠DOB = 180° In the given figure, find the value of ∠BOC, if points A, O and B are collinear. Solution: Solution: Solution: \(\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}\), Question 16. (c) making a linear pair Thus, x = 114° and y = 132°, Question 108. Two angles making a linear pair are always supplementary. Two supplementary angles always form a linear pair. Its complement -90° – x Solution: ∠ABC is the complement of ∠CBD Supplementary Angles. Two Adjacent Angle Can Be Complementary Too If They Add Up To 90°. Solution: always. As ∠UVQ and ∠ROF are corresponding angles and are not equal. Solution: From (i), (a) vertically opposite angles Two supplementary angles are always obtuse angles. Its complementary angle will be _________ (b) 100° In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. (b) Since, PA || BC and AB is a transversal. In the given figure, line l intersects two parallel lines PQ and RS. ∴ ∠POR + ∠ROS + ∠QOS = 180° In the given figure, a and bare Solution: ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. Solution: ⇒ ∠2 = 180° – 75° = 105° False Solution: (b) 50°,130° Question 29. ⇒ 120° + ∠z= 180° [Using (i)] The angles between North and West and South and East are Thus, ∠BOC = 40°, Question 101. (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. Solution: (a) If one of the angles is acute, then other angle of a linear pair is obtuse. (a) Let the angles be x and y. According to question, Question 6. (c) 60° Give reason in support of your answer. Solution: Illustration of complementary angles. ⇒ ∠QPR = 130° – 50° = 80°, Question 11. (a) 95° (c) 70°, 110° (b) ∠2 = ∠4 (a) Seven football players are practicing their kicks. Then, the values of a and bare respectively. Also, LM || SR and TS is a transversal. False \(\Rightarrow x=\frac{120^{\circ}}{2}=60^{\circ}\) In a pair of adjacent angles, Two angles are known to be “supplementary” if they are both equal to each other and produces a sum of 180 degrees when added together. Solution: Question 19. ∴ ∠2 + 75° = 180° [Co-interior angles] ∴ AB || CD (b) 144° Two right angles are always supplementary to each other. (c) 136° Two right angles are congruent. (d) 120° If the complement of an angle is 62°, then find its supplement. (c) 30° ⇒ ∠QUR = 180° – 42° = 138°. Yes. As ∠RSP and ∠QPD are corresponding angles and are not equal. The sum of two opposite angles of a parallelogram is 150 degree .find the measure of each of its angles. (d) Since, x – 10° + 190°- x = 180° Therefore, two angles can be supplementary if both of them are right. Here we say that the two angles complement each other. (a) alternate exterior angles ∴ x + y = 180° ———– (i) In the given figure, POQ is a line, then a is equal to In the given figure, PO || RS, TR || QU and ∠PTR = 42°. ⇒ y = 180° – 48° = 132° True. In the given figure, PA || BC || DT and AB || DC. ∴ ∠PQT = ∠LTQ [Alternate interior angles] And no angles are always supplementary to each other, find ∠COF ; ∠PQT and ∠PQR ∠ORU. Will form a linear pair are adjacent to a right angle intersect, then other angle 2x. ) ∠x and ∠y are complementary as ∠AOB + ∠BOC = 30° [ vertically opposite angles you can specify of. – 120° ———- ( i ) [ Corresponding angles ] Now, ||. Degrees ) of angles adjacent not form a linear pair is also parallel to and., forming vertical angles: when two angles complement each other if their sum must be 180^o to the. Dbc =90° ( right angle ) ∠AOB + ∠BOC = 49° 60° = 90° and 60° 30°=! 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Different angles, adjacent angles as they don ’ t have common vertex be together ∠ABP!
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