Answer
$m \angle X = 52^{\circ}$
Work Step by Step
In two similar triangles, corresponding angles are congruent. Let's list the congruent angles:
$\angle V ≅ \angle P$
$\angle L ≅ \angle S$
$\angle Q ≅ \angle X$
We can now use the triangle sum theorem to find the measure of the third angle, $\angle Q$ of $\triangle VLQ$:
$m \angle Q = 180 - (m \angle V + m \angle L)$
Substitute in what we are given:
$m \angle Q = 180 - (48 + 80)$
Evaluate what's in parentheses first:
$m \angle Q = 180 - (128)$
Subtract to solve:
$m \angle Q = 52^{\circ}$
If $\angle Q ≅ \angle X$, then $m \angle Q = m \angle X$; therefore, $m \angle X = 52^{\circ}$.
