Geometry

Question Analysis

The main focus is applying the Triangle Angle Bisector Theorem. Given that is the angle bisector of in , we need to use the proportional relationship of the sides to find the value of .

 

Key Concept Explanation

The Triangle Angle Bisector Theorem states that if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the other two sides. In , since bisects , we have .

 

Step - by - Step Solution

1. Identify the given values: , , , and .

2. Apply the Triangle Angle Bisector Theorem proportion .

Substitute the known values into the proportion:

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