Question

In the adjoining figure, AP and AQ are tangents to the circle with centre O. If reflex ∠POQ = 210°, the value of 2x is:

विकल्प

• 30°

• 60°

• 120°

• 300°

Answer 1

60°

Explanation:

Given, ∠POQ = 210°, therefore, interior ∠POQ = 360 − 210 = 150°

Also, AP and AQ are tangents to the circle, ∠APO = ∠AQO = 90°

Now, In the quadrilateral, APOQ,

Interior ∠POQ + ∠APO + ∠AQO + ∠PAQ = 360°

150° + 90° + 90° + x = 360°

x = 360° − 330°

x = 30°

∴ 2x = 2 × 30° = 60°