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In the given diagram, we have two parallel lines \( QS \) and \( TV \), and a transversal line \( WRP \) intersecting them. 

To determine which angles are supplementary, we recall that supplementary angles are two angles whose measures add up to 180°. When a transversal crosses two parallel lines, it forms several pairs of supplementary angles, especially consecutive interior angles.

### Let's evaluate the answer choices:

1. **\( \angle TUR \) and \( \angle TUW \)**:
   - These are adjacent angles on the same side of the transversal. Since \( TUW \) is exterior to the parallel lines and \( TUR \) is interior, they are supplementary.

2. **\( \angle TUR \) and \( \angle VUW \)**:
   - These two angles are not consecutive interior angles. Therefore, they are **not supplementary**.

3. **\( \angle TUR \) and \( \angle QRP \)**:
   - These two angles are both interior, but they are **not consecutive**. Thus, they are **not supplementary**.

4. **\( \angle TUR \) and \( \angle SRU \)**:
   - These are consecutive interior angles on the same side of the transversal, making them supplementary.

### Correct Answer:
The angles that are supplementary are:
- **\( \angle TUR \) and \( \angle TUW \)**, and
- **\( \angle TUR \) and \( \angle SRU \)**.

Both pairs are consecutive interior angles or adjacent angles on the same side of the transversal.

Would you like more details about supplementary angles or any other related concept?

Here are five related questions:
1. What are alternate interior angles, and how do they differ from consecutive interior angles?
2. How can we identify corresponding angles when a transversal cuts through parallel lines?
3. How can you prove two lines are parallel using angle relationships?
4. How do adjacent angles relate to linear pairs in geometry?
5. What role do vertical angles play in this kind of diagram?

**Tip**: When dealing with parallel lines and transversals, always look for corresponding, alternate, or consecutive angles to determine relationships between angles.

This problem involves identifying pairs of supplementary angles formed by a transversal cutting through two parallel lines. Students will learn about consecutive interior angles and adjacent angles. Suitable for Grade 8-10 students.

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