Question : In a triangle $\triangle \mathrm{PQR}$, the bisectors of $\angle \mathrm{P}$ and $\angle \mathrm{R}$ meet at a point $\mathrm{M}$ inside the triangle. If the measurement of $\angle P M R=127^{\circ}$, then the measurement of $\angle Q$ is:
Option 1: 90°
Option 2: 74°
Option 3: 180°
Option 4: 106°
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Correct Answer: 74°
Solution :
$\angle PMR = 90° +\frac{1}{2} \angle Q$
⇒ $\angle Q = 2(\angle PMR-90° )$
⇒ $\angle Q = 2(127° -90° )$
⇒ $\angle Q = 2\times 37° $
⇒ $\angle Q = 74° $
Hence, the correct answer is 74°.
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