Thus, the required angles are 60° and 30°. ∴ ∠POR + ∠ROT + ∠TOQ = 180° The sum of two vertically opposite angles is 166°. Find the values of a and b. ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] (a) pair of complementary angles Solution: No, two acute angles cannot form a pair of supplementary angles. alternate interior angles have one common _________ ∴ ∠COD = 90° ⇒ 60° – ∠L ——— (i) 1. 1.Two angles that are complementary never form a linear pair. (c) (108 – b)° ⇒ a = 180° – 100° = 80°. ∴ ∠1 = 30° ——– (i) [Corresponding angles] Solution: (b) 30° Solution: Now, a || d and c is a transversal. Recall that the complementary angle is one that makes the given angle become 90°. \(\Rightarrow a=\frac{50^{\circ}}{5}=10^{\circ}\), Question 27. In the given figure, PQ||RS and a : b = 3 : 2. It is just a complete one angle. (a) Both statements p and q are true. According to question, ⇒ 60° + ∠2 = 180° [Using (ii)] Solution: As, PQ is a straight line. (d) 64° \(\Rightarrow x=\frac{300^{\circ}}{3}=100^{\circ}\) False (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. (b) 90°, 90° Question 24. ⇒ ∠2 = 180° -60° = 120° In the given figure, P, Q and R are collinear points and TQ ⊥ PR, (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. Then, f is equal to (c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles. The value of bis (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. True, Question 62. One of the complementary angles is said to be the complement of the other. In the given figure, the value of y is Now, p || q and n is a transversal. Adding (i) and (ii), we get (a) supplementary From (i) and (ii), we have Distinct. a = ∠1 + ∠2 = 60° + 30° = 90°. ∴ a = f [Corresponding angles] (c) The angle between South and West is a right angle and angle between South and East is also a right angle. (a) 20° ⇒ x = 360°- 210° Statements a and bare as given below: ∴ x + y = 85° + 50° = 135°, Question 41. The angle which makes a linear pair with an angle of 61° is of Explanation: Angle equal to 90 o is called right angle. Thus, d = 142° ⇒ x = 28° Solution: 2. Solution: Now, PQ || RT and RQ is a transversal. ∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. ⇒ x + y = 180° – 90° = 90° (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. Solution: Solution: (d) 10° (i) AB || CD Solution: l || m and PQ is a transversal According to question, ⇒ 4 × 30° = 3b [using (i)] According to question, Solution: ∴ x = 85° [Altemate interior angles] What are the measures of the angle and its supplement? (c) 85° Solution: ⇒ x + 2x = 300° Complementary angles are any two angles that sum to 90°. (d) ∠3 = ∠7 ⇒ 5b + 2 × 40° = 180° Now, AB || DC and BC is a transversal. ⇒ x = 150°, Question 10. Complementary angles are two angles that add up to 90°, or a right angle; two supplementary angles add up to 180°, or a straight angle. (d) ∠2 + ∠3 = 180° Question 67. Now, ∠PQR = ∠PQU + ∠UQR ∴ ∠c + ∠2 = 180° [Linear pair] \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) (c) ∠5 = ∠8 ∴ x + y = 90° ———(i) [Angles are complementary] (ii) each linear pair. a: If two lines intersect, then the vertically opposite angles are equal. Now, a + b = 180° [Angles on a straight line PQ] In each of the following figures, write, if any, ⇒ ∠2 = 180° – 42° – 68° [Using (i)] Then, The two angles do not need to be together or adjacent. Question 112. ∴ ∠HCB =∠CDE [Corresponding angles] Since, l || m and p is a transversal. If the complement of an angle is 62°, then find its supplement. Directions: In questions 1 to 41, there are four options out of which one is correct. False Linear, Question 51. Thus, the required angle is 119°. Two supplementary angles always form a linear pair. 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