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To solve this problem, we need to apply the concept of *corresponding angles* to determine if the lines \( l_1 \) and \( l_2 \) are parallel.

### Step-by-step explanation:

1. **Parallel lines and corresponding angles**:
   When two lines are cut by a transversal, if the corresponding angles are equal, the lines are parallel. In this diagram, the angle labeled as \( x^\circ \) is corresponding to the angle \( 144^\circ \). Therefore, for \( l_1 \) and \( l_2 \) to be parallel, \( x \) must be equal to \( 144^\circ \).

2. **Answer**:
   Since corresponding angles are equal when lines are parallel, the value of \( x \) that proves the lines are parallel is \( x = 144^\circ \).

Thus, the value of \( x \) is:

\[
x = 144^\circ
\]

Would you like more details on the concept of corresponding angles or any related topic?

Here are some additional questions to expand your understanding:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. How can you prove lines are parallel using supplementary angles?
3. What other angle relationships can be used to prove lines are parallel?
4. How does the transversal line affect the angles formed with two parallel lines?
5. What happens if \( x \) and \( 144^\circ \) were not equal—what would that imply about the lines?

**Tip**: Always remember that corresponding angles are located in the same position relative to the transversal and the two lines.

For the diagram below, what value of x will prove l1 and l2 are parallel?

Learn how to find the value of x that proves two lines are parallel using the corresponding angles theorem. This geometry problem covers key concepts related to parallel lines and angles formed by a transversal. Suitable for students in Grades 7-10.

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