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In the diagram provided, two parallel lines, \( TV \) and \( WY \), are intersected by two transversal lines. The question is asking which angles are adjacent.

**Adjacent angles** share a common vertex and a common side, but do not overlap. They are next to each other in the diagram.

Now, looking at the given options:

- \( \angle WXU \) and \( \angle YXZ \): These angles are not adjacent because they do not share a common vertex or side.
- \( \angle WXU \) and \( \angle VUS \): These angles are also not adjacent since they are far from each other.
- \( \angle WXU \) and \( \angle TUS \): These two angles do not share a side or vertex.
- \( \angle WXU \) and \( \angle YXU \): These angles are adjacent because they share the vertex \( X \) and side \( XU \).

Thus, the correct answer is **\( \angle WXU \) and \( \angle YXU \)**.

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### 5 Related Questions:
1. What are supplementary angles, and how are they different from adjacent angles?
2. Can two adjacent angles be supplementary?
3. How do parallel lines and transversals affect the relationship between angles?
4. What are alternate interior and alternate exterior angles?
5. How do you calculate the measure of adjacent angles if one angle's measurement is given?

### Tip:
Adjacent angles always share a common side and vertex, but do not overlap. Identifying them can help in determining relationships like supplementary or complementary angles.

Learn how to identify adjacent angles in diagrams with parallel lines and transversals. This geometry problem focuses on finding angles that share a common vertex and side but do not overlap, suitable for students in Grades 7-9.

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