Let's analyze the given problem step by step.

Observations:

1. Parallel lines: The problem states that parallel lines are cut by a transversal $t$, which results in special angle relationships.
2. Given information: One angle measures $108^\circ$, and the other angle $x$ is to be determined.
3. Options for $m \angle x$: Each option provides a reason for $m \angle x = 72^\circ$ based on angle relationships.

Solution:

When a transversal intersects parallel lines:

• Alternate interior angles are congruent.
• Corresponding angles are congruent.
• Same-side interior angles are supplementary.
• Same-side exterior angles can also form specific relationships.

In the diagram:

1. Angle $108^\circ$ and $x$ are same-side exterior angles.
2. Same-side exterior angles are supplementary, meaning their measures add up to $180^\circ$.

Thus: $x + 108 = 180 \implies x = 180 - 108 = 72^\circ$

Correct Option:

The correct answer is: B. $m \angle x = 72^\circ$ because same-side exterior angles are supplementary.

Would you like a detailed explanation of supplementary angles or angle relationships?

Here are 5 related questions to consider:

1. What are alternate interior angles, and why are they congruent?
2. How can you verify corresponding angles are congruent using geometry rules?
3. What are supplementary angles, and in what cases do they apply?
4. How does the transversal affect the angle relationships when cutting parallel lines?
5. Can angle relationships change if the lines are not parallel?

Tip: Always remember that when parallel lines are involved, their angle relationships simplify geometric problems significantly.