https://file.aiquickdraw.com/mathbot/file/1727108978206x4k5dw1i.jpg

In the image you provided, two lines are intersected by a transversal, forming multiple pairs of angles.

The angles marked \( y \) and \( x \) appear to be opposite each other at the intersection of the two lines. This is a classic case of **vertical angles**, which are congruent (equal in measure).

So, the correct identification for the pair of angles \( y \) and \( x \) is **vertical**.

Would you like further clarification or details on this concept? Here are some related questions to expand your understanding:

1. What are alternate interior angles, and when do they occur?
2. How can you identify corresponding angles in a diagram?
3. What is the difference between alternate interior and alternate exterior angles?
4. Why are vertical angles always congruent?
5. Can you prove that corresponding angles are equal when the lines are parallel?

**Tip**: When two lines are cut by a transversal, angle relationships like vertical, corresponding, and alternate interior/exterior angles help in identifying parallelism and congruence.

Identify each pair of angles in the provided diagram.

Learn how to identify various angle pairs such as vertical, corresponding, alternate interior, and alternate exterior angles in a diagram involving two lines intersected by a transversal. This geometry problem is suitable for students in Grades 7-10.

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