The image you've uploaded shows two parallel lines, $m \parallel n$, with two intersecting transversal lines creating angles. Based on the diagram, we are asked to find the value of $x$.

In the image, the angle formed by the transversal lines crossing line $m$ is $120^\circ$, and the angle at the intersection with line $n$ is labeled as $x$. Since the lines $m \parallel n$ are parallel, the angle $120^\circ$ and angle $x$ are consecutive interior angles, which are supplementary. This means their sum must equal $180^\circ$.

Thus, the equation becomes:

$120^\circ + x = 180^\circ$

Solving for $x$:

$x = 180^\circ - 120^\circ$

$x = 60^\circ$

So, the value of $x$ is $60^\circ$.

Would you like further details or clarification? Here are a few related questions:

1. How do you identify consecutive interior angles in parallel lines?
2. Can you explain the concept of supplementary angles?
3. What other types of angle relationships occur when two lines are parallel?
4. How do transversals affect angle formation with parallel lines?
5. Could this problem change if the lines were not parallel?

Tip: Remember, supplementary angles always add up to $180^\circ$.