Geometry

Question Analysis

This question focuses on using the property of the incenter of a triangle to find the measure of . The key is to utilize the fact that the incenter is the intersection of angle bisectors, and an angle bisector divides an angle into two equal - measure angles.

 

Key Concept Explanation

The incenter of a triangle is the point where the angle bisectors of the triangle intersect. So, the lines from the incenter to the vertices of the triangle bisect the interior angles of the triangle.

 

Step - by - Step Solution

1. Since is the incenter of , the lines , , and are angle bisectors.

2. We are given that .

3. Because is an angle bisector, .

4. So,