Question

In the given figure, PQR is a straight line. Find x. Then complete the following:

(i) ∠AQB = _______
(ii) ∠BQP = _______
(iii) ∠AQR = _______

Answer 1

PQR is a straight line

∠AQP=x + 20°

∠AQB = 2x + 10°

∠BQR = x – 10°

But ∠AQP + ∠AQB + ∠BQR = 180°

⇒ x + 20° + 2x + 10° + x - 10°= 180°

⇒ 4x + 20°= 180°

⇒ 4x = 180° - 20°= 160°

⇒ x = `160^circ/4 = 40^circ`

(i) ∠AQB = 2x + 10° = 2 x 40° + 10° = 80° + 10° = 90°

∠AQP = x + 2(T = 40° + 20° = 60°

∠BQR = x – 10° = 40° – 10° = 30°

(ii) ∠BQP = ∠AQP + ∠AQB = 60° + 90° = 150°

(iii) ∠AQR = ∠AQB + ∠BQR = 90° + 30° = 120°