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.