Triangle Angle Bisector Theorem
An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
By the Angle Bisector Theorem,
Extend to meet at point .
By the Side-Splitter Theorem,
The angles are corresponding angles.
Since is a angle bisector of the angle .
By the Alternate Interior Angle Theorem , .
Therefore, by transitive property, .
Replacing by in equation ( ),
Find the value of .
By Triangle-Angle-Bisector Theorem,
Divide both sides by .
The value of is .