Chapter 4 Angles and Pairs of Angles Practice Set 21 Solutions

Let the measures of ∠A be x°. m∠A = m∠B = x° ∠ACD is the exterior angle of ∆ABC ∴ m∠ACD = m∠A + m∠B ∴ 140 = x + x ∴ 140 = 2x ∴ 2x = 140 ∴ x = = 70 ∴ The measures of the angles ∠A and ∠B is 70° each.

m∠EOD = m∠AOB = 8y ….(vertically opposite angles) ∠FOL, ∠EOD and ∠COD form a straight angle. ∴ m∠FOE + m∠EOD + m∠COD = 180° ∴ 4y + 8y + 6y = 180 ∴ 18y = 180 ∴ y = ∴ y = 10 m∠EOD = 8y = 8 x 10 = 80° m∠AOF = m∠COD ….(Vertically opposite angles) = 6y = 6 x 10 = 60° m∠BOC = m∠FOE ….(Vertically opposite angles) = 4y = 4 x 10 = 40° ∴ The measures of ∠EOD, ∠AOF and ∠BOC are 80°, 60° and 40° respectively.

Let the measure of ∠A be y°. A ∴ m∠A = m∠B = y° ∠ACB and ∠ACD form a pair of linear angles. ∴ m∠ACB + m∠ACD = 180° ∴ (3x – 17) + (8x + 10) = 180 ∴ 3x + 8x – 17 + 10 = 180 ∴ 11x – 7 = 180 ∴ 11x – 7 + 7 = 180 + 7 …(Adding 7 on both sides.) ∴ 11x = 187 ∴ x = = 17 m∠ACB = 3x – 17 = (3 x 17) – 17 = 51 – 17 = 34° m∠ACD = 8x + 10 = 8 x 17 + 10 = 136 + 10 = 146° Here ∠ACD is the exterior angle of ∆ABC and ∠A and ∠B are its remote interior angles. ∴ m∠ACD = m∠A + m∠B ∴ 146 = y + y ∴ 146 = 2y ∴ 2y = 146 ∴ y = = 73 ∴ The measures of ∠ACB, ∠ACD, ∠A and ∠B are 34°, 146°, 73° and 73° respectively.

(Student should attempt the activity on their own)

i. 180° ii. 360° iii. 540° iv. 720° v. 180° x 5 = 900° vi., 180° x 6 = 1080°