In the given problem, lines $m \parallel n$, which indicates that the angles formed are alternate interior angles, a property of parallel lines.

The two angles are given as:

• $(8x + 14)^\circ$
• $(9x - 4)^\circ$

Since these angles are alternate interior angles, they are congruent, meaning their measures are equal. Thus, we can set up the following equation:

$8x + 14 = 9x - 4$

Now, solving for $x$:

1. Subtract $8x$ from both sides: $14 = x - 4$

2. Add 4 to both sides: $18 = x$

So, the value of $x$ is $18$.

Would you like any further details on this solution?

Here are 5 related questions for you:

1. What are the other angle relationships that hold true for parallel lines cut by a transversal?
2. Can alternate exterior angles be used to find $x$ in a similar setup?
3. How would the solution change if the lines were not parallel?
4. What other properties of parallel lines can be used to solve geometric problems?
5. How does the sum of angles on a straight line relate to this problem?

Tip: Always verify angle congruence when dealing with parallel lines and transversals, as they provide straightforward equations for solving unknowns.