To solve for $x$ in the given figure, where $m \parallel n$ (parallel lines), we can use the property of alternate interior angles.

Step-by-Step Solution:

1. Identify the relationship:
   Since $m \parallel n$ and the transversal intersects them, alternate interior angles are congruent (equal).
   Therefore, the angle labeled $110^\circ$ is equal to the angle labeled $x^\circ$.

2. Set up the equation:
   $x = 110^\circ$

3. Conclusion:
   The value of $x$ is: $\boxed{110^\circ}$

Do you need further clarification on alternate interior angles or any related properties? Let me know!

Related Questions to Explore:

1. What are alternate exterior angles, and how are they related to parallel lines?
2. If the transversal creates another angle of $70^\circ$, what would be its corresponding angle on the parallel line?
3. What happens to the angles if the lines $m$ and $n$ are not parallel?
4. How are consecutive interior angles related when two lines are parallel?
5. If a transversal cuts three parallel lines, how does the angle relationship extend?

Tip: Remember, alternate interior angles are always equal when the lines are parallel and cut by a transversal!