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In the given image, we are asked to find which angles are supplementary. The diagram shows two parallel lines \( \overline{SU} \) and \( \overline{VX} \), intersected by a transversal line \( \overline{RXY} \), and possibly another transversal through point \( W \).

**Supplementary angles** are two angles whose measures add up to 180 degrees. In the case of parallel lines cut by a transversal, supplementary angles are often a pair of consecutive (or same-side interior) angles along the transversal.

Let’s review the options and check for supplementary angle pairs:

1. **\( \angle VWY \) and \( \angle STW \)**:
   These two angles are on opposite sides of the transversal, making them alternate interior angles, not supplementary.

2. **\( \angle STR \) and \( \angle VWT \)**:
   These angles do not add up to 180° since they are not consecutive or on the same side of the transversal. This option is incorrect.

3. **\( \angle XWT \) and \( \angle UTR \)**:
   This pair seems to be adjacent angles at point \( T \), forming a straight line. Since adjacent angles on a straight line are supplementary, this pair is correct.

4. **\( \angle XWY \) and \( \angle VWY \)**:
   These two angles share a common side but are not consecutive interior or exterior angles, so they are not supplementary.

Therefore, the correct answer is **\( \angle XWT \) and \( \angle UTR \)**.

Do you want more details on how supplementary angles work in parallel lines, or do you have other questions?

Here are 5 related questions:
1. What are the properties of alternate interior angles in parallel lines?
2. How can you identify consecutive interior angles in a diagram like this?
3. What is the difference between supplementary and complementary angles?
4. Can exterior angles also be supplementary in parallel lines cut by a transversal?
5. How do you calculate the measure of an unknown angle when given a pair of supplementary angles?

**Tip:** When dealing with parallel lines and transversals, look for straight lines and adjacent angles to identify supplementary pairs easily!

Which angles are supplementary in the given diagram of parallel lines SU and VX intersected by transversals?

Learn how to identify supplementary angles in a diagram with parallel lines and transversals. This problem focuses on angle relationships and how to recognize pairs of angles that sum to 180°. Suitable for students in Grades 7-8.

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