To find $x$ so that lines $l$ and $m$ are parallel, we can use the corresponding angles postulate. For lines to be parallel, corresponding angles formed by a transversal must be equal.

In this case:

• The angle $87^\circ$ corresponds to the expression $10x + 17^\circ$ (since they are on the same side of the transversal and in the same relative position).
• The angle $5x^\circ$ appears to be another angle involved, but it doesn't directly correspond to the other two; we will use it if necessary.

Step 1: Set the corresponding angles equal.

$87^\circ = 10x + 17^\circ$

Step 2: Solve for $x$.

Subtract $17$ from both sides:

$87 - 17 = 10x$

$70 = 10x$

Now divide by 10:

$x = 7$

Final Answer:

The value of $x$ is $7$.

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

1. What is the corresponding angles postulate, and how does it apply to parallel lines?
2. If the lines were not parallel, how would the angle relationships change?
3. Can the same value of $x$ be used for different angle configurations in the same diagram?
4. What other angle pairs could help prove that lines are parallel?
5. How would the value of $x$ change if the angle expressions were different?

Tip: When solving for parallel lines, corresponding angles are a key clue to ensure the lines remain parallel!