Question : O is the incentre of the $\triangle \mathrm{PQR}$. If $\angle \mathrm{POR}=120°$, then what is the $\triangle \mathrm{PQR}$?
Option 1: 45°
Option 2: 60°
Option 3: 55°
Option 4: 48°
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Correct Answer: 60°
Solution :
Given, $\angle POR = 120°$
We know, Angle at incentre = $90° + \frac{\text{vertex angle}}{2}$
⇒ $90° + \frac{\angle PQR}{2} = 120°$
⇒ $\frac{\angle PQR}{2} = 120° - 90°$
⇒ $\frac{\angle PQR}{2} = 30°$
⇒ $\angle PQR=60°$
Hence, the correct answer is 60°.
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