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The diagram shows two parallel lines cut by a transversal. The angles marked \( x \) and \( y \) are corresponding angles, and the given angle is 59°.

Let's break down the steps to solve for \( x \) and \( y \):

1. **Find \( x \)**:
   - The angle \( x \) and the given angle (59°) are **alternate interior angles** since they are on opposite sides of the transversal and between the two parallel lines.
   - By the property of alternate interior angles, they are equal. Therefore:
     \[
     x = 59^\circ
     \]

2. **Find \( y \)**:
   - The angle \( y \) and the given angle (59°) are **corresponding angles**, which means they are congruent as well.
   - Therefore:
     \[
     y = 59^\circ
     \]

So, both \( x \) and \( y \) are 59°.

Thus, the answers are:
- \( x = 59 \)
- \( y = 59 \)

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. What are supplementary angles, and how do they relate to this type of problem?
2. How would the solution change if the given angle was 120° instead of 59°?
3. What are corresponding angles, and how can they be identified in other diagrams?
4. Can alternate exterior angles also be equal in such configurations? Why or why not?
5. How do you prove the congruence of corresponding and alternate interior angles?

**Tip**: When working with parallel lines and transversals, always look for corresponding, alternate interior, and alternate exterior angles—they are key to solving for unknown angles.

Find the values of x and y. Given that the lines are parallel and the angles corresponding to x and y are related to the given angle of 59 degrees.

Learn how to solve for angles x and y in a scenario involving parallel lines and a transversal. This problem demonstrates key concepts such as alternate interior angles and corresponding angles, making it suitable for students in Grades 7-9.

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