Answer
$x = 7$
Work Step by Step
According to the angle bisector theorem, if a point is on the bisector of an angle, then that point is equidistant from each side of the angle.
In this diagram, we see an angle bisector and a point on that angle bisector; therefore, the distance from the point to one side of the angle is $5x - 8$, and the distance from the point to the other side of the angle is $2x + 13$. However, these two distances are equal to one another, so we can set them equal to one another:
$5x - 8 = 2x + 13$
Subtract $2x$ from each side of the equation to isolate the variable on the left side of the equation:
$3x - 8 = 13$
Add $8$ to each side of the equation to isolate constants on the right side of the equation:
$3x = 21$
Divide both sides by $3$ to solve for $x$:
$x = 7$
