Answer
$m \angle LKJ = 64$ degrees
Work Step by Step
If the two legs of a triangle are congruent, then that triangle is an isosceles triangle. With isosceles triangles, we need to remember that the base angles are congruent. If $m \angle L$ is $58$, then $m \angle J$ is also $58$. According to the triangle sum theorem, the measures of all the interior angles of a triangle equal $180^{\circ}$.
Now that we have the measures of two of the angles, the last angle can be found. Let's set up that equation:
$m \angle L + m \angle L + m \angle LKJ = 180$
Let's substitute in what we know:
$58 + 58 + m \angle LKJ = 180$
Add the constants on the left side of the equation:
$116 + m \angle LKJ = 180$
Subtract $116$ from both sides of the equation to solve for $m \angle L$:
$m \angle LKJ = 64$
