Answer
$x = 12$
Both $JK$ and $JM$ are $17$.
Work Step by Step
The angle bisector theorem states that a point that is located on an angle's bisector is equidistant from the angle's sides.
In this diagram, we see that $\overline{JL}$ is the angle bisector of $\angle KLM$. Therefore, $J$, which is a point on the bisector, is equidistant from the sides of the angle. So, $L$ is equidistant from $\overline{LK}$ and $\overline{LM}$. Therefore, $\overline{JK}$ is equal to $\overline{JM}$.
Let's set $JK$ and $JM$ equal to one another to find the value for $x$:
$x + 5 = 2x - 7$
Subtract $x$ from each side to isolate the variable on one side of the equation:
$5 = x - 7$
Add $7$ to each side of the equation to solve for $x$:
$x = 12$
$JK = JM = x + 5$
Plug in $12$ for $x$:
$JK = JM = 12 + 5$
Add to solve:
$JK = JM = 17$
