Answer
$\angle XZY$ is congruent to $\angle XBA$ because they are corresponding angles, and corresponding angles are congruent to one another.
Work Step by Step
$\overline{AB}$ joins the midpoint of $\overline{XY}$ and also the midpoint of $\overline{XZ}$. According to the triangle midsegment theorem, if a line segment joins two sides of a triangle at their midpoints, then that line segment is parallel to the third side of that triangle and is half as long as that third side.
Knowing this information, we can deduce that $\overline{YZ}$, which is the third side, is parallel to $\overline{AB}$, which is the line segment that joins the midpoints of the other two sides of the triangle.
Now that we have established that $\overline{ab} \parallel \overline{ab}$, then $\angle XBA$ and $\angle XZY$ are congruent because they are corresponding angles, and corresponding angles are congruent to one another.
