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ICSE Class 10 Mathematics Question 29 of 49

Multiple-Choice Questions — Question 29

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Question

Question 29

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 :

  1. 25°

  2. 40°

  3. 50°

  4. 65°

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 : Maths Competency Focused Practice Questions Class 10 Solutions.
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.