In the given figure, line $m$ is parallel to line $n$, and we need to find the measure of angle $x$.

Here's how we can solve it using properties of parallel lines and transversals:

1. Angle relationships: Since lines $m$ and $n$ are parallel, the angle $124^\circ$ is an exterior angle, and it forms a linear pair with angle $x$. Therefore: $x + 124^\circ = 180^\circ$ This is because the two angles are supplementary (they form a straight line).

2. Solve for $x$: $x = 180^\circ - 124^\circ = 56^\circ$

Now we check the options. The correct answer does not appear to match directly, but a further review might clarify if there's a misinterpretation.

Would you like to go over the steps or clarify the diagram further?

Here are 5 related questions to explore this concept:

1. What are alternate interior angles, and how do they apply to parallel lines?
2. How do corresponding angles behave with parallel lines and a transversal?
3. How do you calculate the measure of angles formed by intersecting lines?
4. What is the sum of the interior angles of a triangle?
5. How do supplementary and complementary angles differ?

Tip: When lines are parallel, angles formed by transversals exhibit predictable relationships like alternate interior, corresponding, and consecutive interior angles.