Given that the two lines, $m$ and $n$, are parallel ($m \parallel n$), and you are asked to find the value of $x$, you can use the fact that corresponding angles formed by a transversal intersecting two parallel lines are equal.

Setup:

• The angle on one line is $(5x - 24)^\circ$.
• The angle on the other line is $(6x + 6)^\circ$.

Since the lines are parallel, and these angles are corresponding angles, we set them equal to each other:

$5x - 24 = 6x + 6$

Solve for $x$:

1. Subtract $5x$ from both sides: $-24 = x + 6$

2. Subtract 6 from both sides: $-24 - 6 = x$ $x = -30$

Thus, the value of $x$ is $\mathbf{-30}$.

Would you like more details or have any other questions?

Here are five related questions to explore further:

1. How can you identify corresponding angles when parallel lines are involved?
2. What is the relationship between alternate interior angles in parallel lines?
3. How would the equation change if the angles were supplementary instead of equal?
4. Can corresponding angles be unequal if the lines are not parallel?
5. What other types of angle pairs exist when a transversal crosses parallel lines?

Tip: Always check if the angles are corresponding, alternate interior, or exterior when dealing with parallel lines!