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Given that \( m \parallel n \), we can use the properties of parallel lines and angles to find the values of \( x \) and \( y \).

1. **Corresponding angles**: Since \( m \parallel n \) and the transversal crosses both lines, the angle labeled \( x^\circ \) is corresponding to the angle labeled \( y^\circ \). Therefore, \( x = y \).

2. **Supplementary angles**: The angle adjacent to \( x^\circ \) is \( 130^\circ \), and these two angles form a straight line. Therefore, they are supplementary, meaning their sum is \( 180^\circ \). So, we can set up the following equation:
   \[
   x + 130^\circ = 180^\circ
   \]
   Solving for \( x \):
   \[
   x = 180^\circ - 130^\circ = 50^\circ
   \]
   Since \( x = y \), we also have \( y = 50^\circ \).

Thus, the values of \( x \) and \( y \) are both \( 50^\circ \).

Would you like further details or have any questions? Here are 5 related questions:

1. What are alternate interior angles in parallel lines?
2. How do you determine angles in parallel lines cut by a transversal?
3. What other types of angles are formed when a transversal cuts parallel lines?
4. What is the sum of the angles on a straight line?
5. What is the definition of corresponding angles?

**Tip**: When dealing with parallel lines, always look for angle relationships like corresponding, alternate, or co-interior angles to simplify your work.

This geometry problem asks to find the values of angles x and y when two parallel lines are cut by a transversal. Using the corresponding angles postulate and supplementary angles theorem, you will learn how to solve for the unknown angles. Suitable for students in Grades 7-9.

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