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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.

Solve for m∠WXY given that ∠WXZ = 52° and ∠ZXY = 38°.

Learn how to solve for m∠WXY by adding angles ∠WXZ and ∠ZXY. The solution uses the Angle Addition Postulate, and is suitable for students in Grades 6-8. In this case, m∠WXY is the sum of 52° and 38°, resulting in 90°.

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