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

1.	In the given figure, PQR is a straight line. Find x. Then complete the following:(i) ∠AQB = ……..(ii) ∠BQP = ……..(iii) ∠AQR = …….
Answer» 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 = (160/4)° = 40° (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°

In the given figure, PQR is a straight line. Find x. Then complete the following:(i) ∠AQB = ……..(ii) ∠BQP = ……..(iii) ∠AQR = …….

Answer»

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 = (160/4)° = 40°

(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°