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The image shows a problem asking to find the measure of angle \( \angle ZYN \), given that lines \( PQ \parallel MN \), and two expressions for the angles involving \( X \) and \( Z \).

### Given Information:
- \( \angle WXY = (11x - 25)^\circ \)
- \( \angle ZYN = (7x + 25)^\circ \)
- \( PQ \parallel MN \), meaning we can apply the properties of parallel lines and transversals, particularly corresponding and alternate interior angles.

### Solution Strategy:

1. **Corresponding Angles:** Since \( PQ \parallel MN \), angle \( \angle WXY \) corresponds to angle \( \angle ZYN \). Corresponding angles are congruent, so:
   \[
   11x - 25 = 7x + 25
   \]

2. **Solve for \( x \):**
   \[
   11x - 7x = 25 + 25
   \]
   \[
   4x = 50
   \]
   \[
   x = 12.5
   \]

3. **Find \( \angle ZYN \):**
   Substitute \( x = 12.5 \) into the expression for \( \angle ZYN \):
   \[
   \angle ZYN = 7(12.5) + 25 = 87.5 + 25 = 112.5^\circ
   \]

Thus, the measure of \( \angle ZYN \) is \( 112.5^\circ \).

Would you like more details on how the properties of parallel lines were used? Here are some related questions:

1. What are corresponding angles, and how do they relate to parallel lines?
2. Can you provide more examples of problems involving transversals and parallel lines?
3. How do alternate interior angles function when lines are parallel?
4. What if \( PQ \) and \( MN \) were not parallel—how would that change the problem?
5. How can you verify if two angles are congruent in parallel line problems?

**Tip:** In parallel line problems, always check if alternate interior or corresponding angles are congruent. This can greatly simplify finding unknown angles.

Learn how to find the measure of angle ∠ZYN when given PQ || MN using corresponding angles. The problem covers concepts related to parallel lines, transversals, and algebraic methods for solving linear equations.

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