https://file.aiquickdraw.com/mathbot/file/1726357838779r1x0lvtj.jpg

This image shows a diagram with two parallel lines, \( m \parallel n \), and a transversal intersecting both lines, creating angles of 108° and \( x^\circ \).

### Step-by-Step Solution:
1. **Identify the relationship between angles**:
   - Since lines \( m \) and \( n \) are parallel, the angle of 108° and angle \( x^\circ \) are **corresponding angles**.
   - Corresponding angles are equal when two parallel lines are cut by a transversal.

2. **Apply the rule**:
   - Since the corresponding angles are equal, we have:
     \[
     x = 108^\circ
     \]

Thus, the value of \( x \) is:
\[
\boxed{108^\circ}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What are alternate interior angles, and how do they differ from corresponding angles?
2. How can you determine angles formed by a transversal cutting parallel lines using vertical angles?
3. If one of the angles were changed to 72°, how would you find the corresponding or alternate angles?
4. Can the transversal form supplementary angles with the angles formed by the parallel lines? If so, how?
5. How do you prove that the lines are parallel given specific angle relationships?

**Tip**: When working with parallel lines and a transversal, it's useful to remember that corresponding angles are always equal, and alternate interior angles are also equal.

Learn how to determine the value of x when two parallel lines are intersected by a transversal, creating corresponding angles. In this problem, one angle is 108°, and the other is x°. The solution involves using the Corresponding Angle Theorem.

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