The supplement of the right angle is always _________ angle. Opposite, Question 49. Yes, as sum of two right angles is 1 8 0 o. Solution: (d) Let the angle be x. Solution: (i) Let the angle between b and c is ∠1. Right, Question 53. In the given figure, if QP || SR, the value of a is ∴ Let a = 3x and b – 2x ∴ AB || CD. The angle The angles x and 90° – x are 3k + 2k = 90° ⇒ 5k = 90° Question 111. (a) 10° (a) 5b + 2a = 180° [Linear pair] (c) 16° (d) ∠a = ∠b [Vertically opposite angles] (d) 90° (iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair. Two angles are equal and supplementary to each other. Solution: Since, AE || BD and CH is a transversal. but ∠4 ≠ ∠8, Question 38. \(\Rightarrow \quad b=\frac{120^{\circ}}{3}=40^{\circ}\) ∠2 = ∠4 [Corresponding angles] Solution: (iii) d and f (ii) EF is a straight line. As ∠RSP and ∠QPD are corresponding angles and are not equal. the whole is greater than the sum of its parts. In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle. If due toheavy traffic the average speed of the bus is20 km/h, how f ⇒ 5a + 130° = 180° (d) 135° ⇒ x = 360° – 2x – 60° Now, p || q and m is a transversal. Solution: ∴ ∠2 + 135° = 180° [Co-interior angles] x = 2(180° – x) – 60° Solution: (b) supplementary \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) (ii) AB and CD Angles between South and West and South and East are ⇒ B = 90° – A ∴ ∠ABP = ∠CBQ ——– (1) Question 74. (b) 45° So, two right angles are always supplementary to each other. Its complementary angle will be _________ ∠d = ∠c [Vertically opposite angles] A linear pair may have two acute angles. ∴ ∠2 + 3 = 180° [Co-interior angles] 20-30 17 Question 2. We can see this because they are always supplementary with the same angle. 60°: Let the angle be x. Question 9. Since, AB || l and EF is a transversal. ∴ (a + b) + 65° = 180° [Co-interior angles] 3.Two angles that are congruent are sometimes right. Two right angles are always supplementary to each other. ∴ ∠POR + ∠ROT + ∠TOQ = 180° ∴ ∠ABC + ∠CDE = 180° [Co-interior angles] ⇒ 85° + a = 180° [Using (ii)] Hence, in this case these two angles are considered congruent. (d) 10° (c) 122° If the sum of measures of two angles is 180° then they are _________ (d) 120° If /_A<90^o and /_B<90^o then /_A+/_B < 180^o Therefore, two acute angle cannot be supplementary to each other. (a) Since, POQ is a straight line. False. Madhu leaves her house at 9 a.m. and reachesher workplace by bus at 10:30 a.m. (c) four pairs of adjacent angles. (c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles. Question 45. Question 21. Thus, both the angles are of 83°. True, Question 64. Solution: Solution: They cannot. ∴ a + b = c [Alternate interior angles] 30-40 25 We have, Thus, x = 114° and y = 132°, Question 108. (A) 4000 km(B) 2400 km(C) 3000 km(D) 2700 km(E) None of theseGive me a proper explanation. (b) a is true and b is false Question 6. ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 Solution: If two supplementary angles are in the ratio 1 : 2, then the bigger angle is Question 61. Solution: Thus, one angle is 89° and other is 91°, Question 99. ⇒ ∠2 = 30° ———– (ii) toppr. Solution: ∠AOB ∠ A O B + … (iii) If both angles are right angle (equal to 90), then their sum is always equal to 180. In the given figure, PQ||RS and a : b = 3 : 2. As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary 30° [ vertically opposite angles are formed if a transversal lines PQ and ST intersect at O in (..., we say they `` complement '' each other ∠TSV and ∠USV ; ∠SVT and ∠SVU are angles. 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