Solution:

Given that m is parallel to n (denoted by m ‖ n), the transversal line creates alternate interior angles and corresponding angles.

Step 1: Finding $y$

The given angle is $47^\circ$, and it forms a pair of corresponding angles with $y$ because of the parallel lines.
Thus, by the corresponding angles theorem:
$y = 47^\circ$

Step 2: Finding $x$

Since $x$ and $y$ are on a straight line, they are supplementary angles.
The sum of angles on a straight line is $180^\circ$.
Thus: $x + y = 180^\circ$ Substitute $y = 47^\circ$: $x + 47^\circ = 180^\circ$ Solve for $x$: $x = 180^\circ - 47^\circ$ $x = 133^\circ$

Final Answer:

• $x = 133^\circ$
• $y = 47^\circ$

Would you like a more detailed explanation or a diagram? Let me know if you need further help!

Related Questions:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. What is the difference between corresponding angles and vertical angles?
3. How do you prove two lines are parallel using transversal angles?
4. How do supplementary angles work in other geometric shapes?
5. How can we solve for unknown angles in a triangle using parallel lines?

Tip: When solving geometry problems with parallel lines, always look for corresponding, alternate interior, or supplementary angles.