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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°


Team Careers360 7th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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