To solve for $x$ and $y$ in the given figure with parallel lines $l \parallel g$:

Step 1: Analyze the Angles

Since $l \parallel g$, the corresponding angles formed by the transversal lines are equal. In this case:

1. The angle labeled $x^\circ$ and the angle marked as $75^\circ$ are corresponding angles, so $x = 75$.
2. The angle $(5y - 10)^\circ$ and the angle marked as $75^\circ$ are also corresponding angles, so $5y - 10 = 75$.

Step 2: Solve for $x$

From our analysis: $x = 75$

Step 3: Solve for $y$

Using the equation $5y - 10 = 75$:

1. Add 10 to both sides: $5y = 85$
2. Divide by 5: $y = 17$

Summary of Solutions:

• $x = 75$
• $y = 17$

Would you like further details on any part of this solution?

Here are some related questions to expand understanding:

1. How do corresponding angles work in parallel lines?
2. What other properties of angles can be used with parallel lines?
3. How can alternate interior angles help in solving such problems?
4. What are the consequences of two lines being parallel in geometry?
5. How can you verify if two lines are parallel based on angle measures?

Tip: Always look for corresponding or alternate interior angles when working with parallel lines and a transversal.