Geometry

Question Analysis

This question focuses on using the property of the incenter of a triangle to find the measure of , testing knowledge of angle bisectors and the incenter.

 

Key Concept Explanation

The incenter of a triangle is the point of intersection of the angle bisectors. If we know the measures of the angles that are bisected by the lines from the incenter, we can find the measure of the whole angle.

 

Step - by - Step Solution

1. Since  is the incenter of , the lines from  to the vertices are angle bisectors.

2. We know that  is composed of two angles that are bisected by the incenter - related lines. Given  and .

3. The incenter bisects the angles of the triangle. So

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