In this problem, we are given two parallel lines $m \parallel n$, cut by a transversal $t$. The two given angles, $(5x + 8)^\circ$ and $(6x - 18)^\circ$, are alternate interior angles. Since the lines are parallel, alternate interior angles are congruent. Thus, we can set the expressions for these angles equal to each other:

$5x + 8 = 6x - 18$

Solving for $x$:

1. Subtract $5x$ from both sides: $8 = x - 18$

2. Add 18 to both sides: $26 = x$

Thus, the value of $x$ is:

$x = 26$

Would you like more details or have any other questions?

Related questions:

1. What is the definition of alternate interior angles?
2. How would the equation change if the angles were supplementary instead of congruent?
3. Can alternate exterior angles be used in a similar problem setup? Why or why not?
4. How do parallel lines affect angle relationships when a transversal is introduced?
5. If the angles were corresponding instead, what equation would be set up?

Tip:

Always remember that for parallel lines cut by a transversal, corresponding angles, alternate interior angles, and alternate exterior angles are congruent.