To solve for $x$, given that lines $m \parallel n$, we can use the fact that alternate interior angles are congruent when two parallel lines are intersected by a transversal. In the diagram, $5x - 14$ and $4x + 4$ are alternate interior angles, so we can set them equal to each other.

Step-by-Step Solution

1. Set up the equation: $5x - 14 = 4x + 4$

2. Move $4x$ to the left side by subtracting $4x$ from both sides: $x - 14 = 4$

3. Add 14 to both sides to isolate $x$: $x = 18$

Final Answer

The value of $x$ is: $x = 18$

Would you like further details on why alternate interior angles are congruent or have any other questions?

Related Questions:

1. What are alternate interior angles, and why are they equal in this case?
2. How would the solution change if the lines were not parallel?
3. Can this concept of congruent angles be applied to other types of angle pairs, such as corresponding angles?
4. What other types of angle relationships occur with parallel lines and a transversal?
5. How can we verify our solution by substituting $x = 18$ back into the angle expressions?

Tip:

Remember that alternate interior angles are congruent when two parallel lines are intersected by a transversal. This is a helpful property in many geometry problems!