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 E.
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 AE by AB in equation (1),
Find the value of x.
By Triangle-Angle-Bisector Theorem,
5x = 42
Divide both sides by 5.
The value of x is 8.4.