## Geometry: Common Core (15th Edition)

$x = 5$
The converse of the angle bisector theorem states that a point inside an angle that is equidistant from the two sides of the angle is located on the bisector of that angle. In this diagram, we see that $\overline{WY}$ is equidistant from the two sides of $\angle TWZ$, so $\overline{WY}$ is the angle bisector of $\angle TWZ$. $2x = 3x - 5$ Subtract $2x$ from each side of the equation to isolate the variable on the left side of the equation: $0 = x - 5$ Add $5$ to each side to solve for $x$: $x = 5$