In the given figure, AOB is a straight line. Find the value of x and a

1.	In the given figure, AOB is a straight line. Find the value of x and also answer each of the following :(i) ∠AOP = ……..(ii) ∠BOP = ……..(iii) which angle is obtuse ?(iv) which angle is acute ?
Answer» ∠AOP = x + 30° ∠BOP = x – 30° But ∠AOP + ∠BOP = 180° (∵ ∠AOB is a straight angle) ⇒ x + 30°+ x - 30° = 180° ⇒ 2x = 180° ⇒ x = 90° (i) ∠AOP = x + 30° = 90° + 30° = 120° (ii) ∠BOP = x- 30° = 90° – 30° = 60° (iii) ∠AOP is an obtuse angle (iv) ∠BOP is an acute angle

In the given figure, AOB is a straight line. Find the value of x and also answer each of the following :(i) ∠AOP = ……..(ii) ∠BOP = ……..(iii) which angle is obtuse ?(iv) which angle is acute ?

Answer»

∠AOP = x + 30°

∠BOP = x – 30°

But ∠AOP + ∠BOP = 180° (∵ ∠AOB is a straight angle)

⇒ x + 30°+ x - 30° = 180°

⇒ 2x = 180°

⇒ x = 90°

(i) ∠AOP = x + 30° = 90° + 30° = 120°

(ii) ∠BOP = x- 30° = 90° – 30° = 60°

(iii) ∠AOP is an obtuse angle

(iv) ∠BOP is an acute angle