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To determine the correct answer, we need to analyze the relationship between angle \( x \) and the \( 108^\circ \) angle. The diagram shows two parallel lines cut by a transversal, which creates various angle relationships:

1. **Alternate Interior Angles**: Angles that are on opposite sides of the transversal and inside the parallel lines. These angles are congruent.
2. **Corresponding Angles**: Angles that are on the same side of the transversal and in corresponding positions. These angles are also congruent.
3. **Same-Side Exterior Angles**: Angles on the same side of the transversal and outside the parallel lines. These are supplementary, meaning their measures add up to \( 180^\circ \).
4. **Vertical Angles**: Angles directly opposite each other at an intersection, which are congruent.

Given:
- The angle marked \( 108^\circ \) is an exterior angle.
- \( x^\circ \) is on the same side of the transversal as the \( 108^\circ \) angle and also an exterior angle.

Since \( x^\circ \) and \( 108^\circ \) are on the same side of the transversal and exterior, they are **same-side exterior angles** and are therefore **supplementary**. 

### Calculation:
Since \( x^\circ \) and \( 108^\circ \) are supplementary:
\[
x + 108 = 180
\]
\[
x = 180 - 108 = 72^\circ
\]

The correct answer is:
**C. \( m \angle x = 72^\circ \) because same side exterior angles are supplementary.**

Would you like more details, or have any other questions?

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Here are some related questions:
1. What are alternate interior angles, and how are they used in geometry?
2. How do you identify corresponding angles in a diagram with parallel lines and a transversal?
3. What is the difference between supplementary and congruent angles?
4. Can you explain how vertical angles are formed and why they are congruent?
5. How do same-side interior angles differ from same-side exterior angles?

**Tip**: When dealing with parallel lines and transversals, identifying angle relationships helps in solving for unknown angles quickly.

Parallel lines cut by a transversal form special angle pair relationships. Which statement is true about the measure of angle x?

Learn how to find the measure of angle x when parallel lines are cut by a transversal, using the Same-Side Exterior Angles Theorem. This problem demonstrates key concepts in angle relationships and geometry, suitable for students in Grades 8-10.

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