In a triangle PQR, incentre is A and ∠QAR = 116°. Find the measure of ∠QPR.

Correct option is D

Given:

In triangle PQR, the incenter is

​$$\angle QAR = 116^\circ,$$​​

Concept Used:

If PQR is a triangle and A is the incenter, then:

​$$\angle QAR = 90^\circ + \frac{\angle P}{2}$$​​

Solution:

​$$\angle QAR = 90^\circ + \frac{\angle P}{2}$$​

Given that $$\angle QAR = 116^\circ,$$​ we substitute into the equation:

​$$116^\circ = 90^\circ + \frac{\angle P}{2}$$​

​$$26^\circ = \frac{\angle P}{2}$$​​

​$$∠P = 52^\circ$$​​