Mathematics
In the adjoining figure, O is the center of the circle, and a semicircle is drawn on OA as the diameter. ∠APQ = 20°. The degree measure of ∠OAQ is :
25°
40°
50°
65°
Circles
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Answer
We know that,
Angle in a semi-circle is a right angle.
∴ ∠OQA = 90°
In △QAP,
⇒ ∠PQA + ∠QAP + ∠APQ = 180°
⇒ 90° + ∠QAP + 20° = 180°
⇒ ∠QAP = 180° - 90° - 20° = 70°.
In △OPA,
⇒ OA = OP (Radii of same circle)
⇒ ∠OAP = ∠OPA (Angle opposite to equal sides are equal)
⇒ ∠OAP = 20°.
From figure,
⇒ ∠OAQ = ∠QAP - ∠OAP = 70° - 20° = 50°.
Hence, Option 3 is the correct option.
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