Answer
$TW = 10$
Work Step by Step
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 $\angle TWZ$.
Corresponding parts of congruent triangles are congruent; therefore, $\overline{WT}$ and $\overline{WZ}$ are congruent, so we can set them equal to one another to find $x$:
$2x = 3x - 5$
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 $x$:
$x = 5$
Now that we have the value for $x$, we can substitute it into the expression for $TW$:
$TW = 2x$
Substitute $5$ for $x$:
$TW = 2(5)$
Solve by multiplying:
$TW = 10$
