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?

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.