Question

In the adjoining figure, O is the centre of the circle and a semicircle is drawn on OA as the diameter. ∠APQ = 20°. The degree measure of ∠OAQ is:

विकल्प

• 25°

• 40°

• 50°

• 65°

Answer 1

50°

Explanation:

The angle at the centre subtending the same arc is twice the angle at the circumference.

So, ∠AOQ = 2 × ∠APQ 

= 2 × 20°

= 40°

Q lies on the semicircle with OA as diameter.

So, the angle subtended by OA at Q is 90°. 

i.e. ∠AQO = 90°

In triangle AOQ:

∠OAQ = 180° – ∠AOQ – ∠AQO

= 180° – 40° – 90°

= 50°

Thus, ∠OAQ = 50°.