The problem in the image asks to "find the value of $x$ so that lines $l \parallel m$." It also requests that you "state the converse used."

From the diagram provided, we have two angles that involve $x$:

• One angle is labeled as $87^\circ$.
• The other angle is expressed as $(10x + 17)^\circ$.

These angles are corresponding angles because they lie on the same side of the transversal cutting the parallel lines $l$ and $m$. When two lines are parallel, corresponding angles are equal. This gives us the equation:

$10x + 17 = 87$

Solving for $x$:

$10x + 17 = 87$ Subtract 17 from both sides: $10x = 70$ Divide by 10: $x = 7$

Thus, the value of $x$ is 7.

Converse used:

The converse of the Corresponding Angles Postulate states that if two corresponding angles are congruent, then the lines are parallel.

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

1. What are corresponding angles, and how do they help prove parallelism?
2. Can you explain the Corresponding Angles Postulate in more detail?
3. How would the solution change if the angles were alternate interior angles instead?
4. What is the difference between the converse of a theorem and the theorem itself?
5. Could you apply a similar method to solve for parallelism using vertical angles?

Tip:

When dealing with parallel lines and transversals, always check the relationships between angles (corresponding, alternate interior, or consecutive interior) to help solve for unknown variables.