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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:
Options
25°
40°
50°
65°
MCQ
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Solution
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°.
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