We are given a diagram with angles labeled at point $X$, and we are asked to solve for $m \angle WXY$. Here's how we can proceed:

Step-by-step Solution:

1. In the diagram, we are given two angles around point $X$:

   • $\angle WXZ = 52^\circ$
   • $\angle ZXY = 38^\circ$

2. The total angle $\angle WXY$ is made up of the sum of these two angles. Therefore: $m \angle WXY = m \angle WXZ + m \angle ZXY$

3. Substituting the given values: $m \angle WXY = 52^\circ + 38^\circ = 90^\circ$

Thus, the measure of $\angle WXY$ is $90^\circ$.

Would you like more details or have any questions on this? Here are some related questions:

1. How are adjacent angles calculated?
2. What is a right angle and how is it represented in geometry?
3. What is the sum of angles on a straight line?
4. How do supplementary and complementary angles differ?
5. Can you explain how angles around a point are summed?

Tip: In geometric problems, always check if angles form special combinations (like right angles, straight angles, etc.) to simplify calculations.