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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.

In the figure below, line m is parallel to line n. What is the measure of ∠x?

Learn how to solve for the unknown angle ∠x using the properties of parallel lines and supplementary angles. The problem involves finding the relationship between angles formed by a transversal and parallel lines, suitable for students in Grade 8-10.

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