The image shows two parallel lines, $m \parallel n$, cut by a transversal. The angles labeled are $x^\circ$ and $118^\circ$. To find the value of $x$, we can use the fact that corresponding angles are equal when two parallel lines are cut by a transversal.

Since $m \parallel n$, the angle $x^\circ$ and the angle labeled $118^\circ$ are supplementary angles (they form a straight line at the intersection of the transversal). Therefore, their sum must be 180°.

Using the equation: $x + 118 = 180$ $x = 180 - 118 = 62^\circ$

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

Would you like further details or have any questions?

Here are some related questions to consider:

1. What are corresponding angles in parallel lines?
2. How can you identify alternate interior angles with parallel lines?
3. What is the difference between supplementary and complementary angles?
4. How do you prove that two lines are parallel using angles formed by a transversal?
5. What are the properties of vertically opposite angles?

Tip: When dealing with parallel lines and a transversal, always check if the angles are corresponding, alternate interior, or supplementary to simplify calculations.