Question

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 1

∠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.