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In a ΔPQR, the bisectors of ∠Q and ∠R meet at point O, inside the triangle. If ∠QOR = 107°, then the measure of ∠P is:

SSC · 2024 · Quantitative Aptitude
Question:
In a ΔPQR, the bisectors of ∠Q and ∠R meet at point O, inside the triangle. If ∠QOR = 107°, then the measure of ∠P is:

Options

(1) 40°
(2) 23°
(3) 17°
(4) 34°
Answer: (4) 34°

Explanation:
∠QOR = 90° + ∠P/2. So 107° = 90° + ∠P/2. Therefore ∠P/2 = 17°, ∠P = 34°.

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