PQ is the diameter of a circle. Two points M and N lie on opposite sides of the diameter PQ such that ∠PMN = 30°. R is a point on the minor arc QN. Find the measure of ∠QRN (in degrees).
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Correct answer: A
Explanation
Given: ∠PMN = 30°.
Arc PN = 2 × 30° = 60°.
In the semicircle:
Arc PQ = 180° (since PQ is the diameter).
Arc QN = 180° - 60° = 120°.
Since R lies on the minor arc QN, ∠QRN subtends the major arc QN.
Major arc QN = 360° - 120° = 240°.
Inscribed angle = half of the arc.
∠QRN = 1/2 × 240° = 120°.