Question

In the above figure, if ∠P = 50°, then reflex angle AOB is ______.

विकल्प

• 2 × 50°

• 180° − 60°

• 230°

• none of these

Answer 1

In the above figure, if ∠P = 50°, then reflex angle AOB is 230°.

Explanation:

Join OB.

We know that,

Tangent at any point of a circle and the radius through this point are perpendicular to each other.

∴ ∠OAP = 90° and ∠OBP = 90°

In quadrilateral OAPB,

⇒ ∠OAP + ∠APB + ∠PBO + ∠AOB = 360°

⇒ 90° + 50° + 90° + ∠AOB = 360°

⇒ ∠AOB + 230° = 360°

⇒ ∠AOB = 360° − 230° = 130°

Reflex ∠AOB = 360° − ∠AOB = 360° − 130° = 230°