In the image, we are given two parallel lines, $m \parallel n$, and a transversal that intersects both lines, forming angles. We are asked to find the value of $x$.

Here's how we can approach it:

1. The angle labeled as $118^\circ$ is given, and it is on one side of the transversal.
2. The angle $x^\circ$ is on the opposite side of the transversal and inside the parallel lines.

These two angles are supplementary, meaning their sum is $180^\circ$, because they form a linear pair (they are same-side interior angles due to the parallel lines).

Thus, we can write the equation: $x + 118^\circ = 180^\circ$

Solving for $x$: $x = 180^\circ - 118^\circ = 62^\circ$

Therefore, the value of $x$ is $62^\circ$.

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions:

1. What are alternate interior angles in parallel line theorems?
2. Can two angles on the same side of a transversal be congruent?
3. What is the difference between corresponding angles and supplementary angles?
4. How do you solve for an unknown angle when both parallel lines and a transversal are involved?
5. What is the definition of a linear pair of angles?

Tip: When dealing with parallel lines and transversals, look for angle pairs like corresponding, alternate interior, or supplementary angles to make solving easier.