## Geometry: Common Core (15th Edition)

$x = 10$
According to the triangle-angle-bisector theorem, when a ray bisects the angle of a triangle, the opposite side is divided into two segments that are proportional to the remaining two sides of the triangle. Let's set up a proportion that compares the segments of the intersected side to the other two sides: $\frac{6}{x} = \frac{12}{20}$ Use the cross product property to get rid of the fractions: $12x = 120$ Divide each side of the equation by $12$ to solve for $x$: $x = 10$