Multiple choice

In a circle, O is the center and PQ is any chord and M is the point on the major arc. If angle ∠ PMQ = 75o then find the value of angle ∠OQP. एक गोले में O केंद्र तथा PQ एक जीवा है तथा M ऋजुचाप पर एक बिंदु है । यदि कोण ∠ PMQ = 75o है, तो कोण ∠OQP का मान ज्ञात कीजिये ।

  1. 15o

  2. 150o

  3. 75o

  4. 30o
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A Correct answer
Explanation

Angle PMQ is an inscribed angle subtending arc PQ. Since M is on the major arc, angle POQ (central angle) = 2 × 75° = 150°. In triangle OPQ (isosceles with OP = OQ), angle OQP = (180° - 150°)/2 = 15°.

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