In the given diagram, we see two pairs of parallel lines: $k \parallel l$ and $m \parallel n$. There are two unknowns, $y^\circ$ and $x^\circ$, that we need to find.

Let's break this down using angle relationships.

Step 1: Identifying Angle $y^\circ$

The angle labeled as $68^\circ$ is formed by the transversal cutting across the parallel lines $k \parallel l$. This makes the angle $y^\circ$ an alternate interior angle with respect to the $68^\circ$ angle. Since alternate interior angles are equal when lines are parallel: $y = 68^\circ$

Step 2: Identifying Angle $x^\circ$

Now, observe the angle $x^\circ$ and the $68^\circ$ angle. These two angles form a linear pair because they are on the same line and adjacent. A linear pair sums up to $180^\circ$: $x + 68^\circ = 180^\circ$ Solving for $x$: $x = 180^\circ - 68^\circ = 112^\circ$

Final Answer:

$y = 68^\circ, \quad x = 112^\circ$

Would you like any additional details or clarification on these steps?

Here are some related questions to explore further:

1. What are alternate interior angles, and how do they help solve problems with parallel lines?
2. How do you identify corresponding angles in parallel line diagrams?
3. What is the sum of angles in a linear pair, and how does it help find unknown angles?
4. How would this problem change if the lines were not parallel?
5. What are other common angle relationships formed by parallel lines and a transversal?

Tip: Always remember that angles on a straight line (linear pair) add up to 180 degrees!