Answer
$m \angle KHL$ is $54^{\circ}$.
$m \angle KHL$ is $54^{\circ}$.
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 the ray $HL$ is equidistant from the two sides of $\angle KHF$, so ray $HL$ is the angle bisector of $\angle KHF$. Therefore, $\angle KHL$ and $\angle FHL$ are congruent. So we can set the two angles equal to one another to solve for $y$:
$6y = 4y + 18$
Subtract $4y$ from each side of the equation to isolate the variable on the left side of the equation:
$2y = 18$
Divide each side of the equation by $2$ to solve for $y$:
$y = 9$
Now that we have the value for $y$, we can substitute it into the expression for one of the angles because the angles are the same:
$m \angle KHL = 6y$
Substitute $9$ for $y$:
$m \angle KHL = 6(9)$
Solve by multiplying:
$m \angle KHL = 54^{\circ}$
If $m \angle KHL$ is $54^{\circ}$, then $m \angle KHL$ is also $54^{\circ}$.
