Geometry

Question Analysis

This question combines the concept of an angle bisector with algebraic equation - solving.

 

Key Concept Explanation

An angle bisector is a ray that divides an angle into two congruent angles. So, if  bisects , then , and .

 

Step - by - Step Solution

1. Set up the equation based on the angle - bisector property:

Given  and , we have .

Expand the left - hand side using the distributive property: .

 

2. Solve the equation for :

Move the  terms to one side. Subtract  from both sides: