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In the image, you are asked whether lines \( l \) and \( m \) are parallel, given two angles: \( 50^\circ \) and \( 130^\circ \).

To determine if lines \( l \) and \( m \) are parallel, we can apply the **Converse of the Consecutive Interior Angles Theorem** (also known as the **Same-Side Interior Angles Theorem**). This theorem states that if the sum of the same-side interior angles equals \( 180^\circ \), then the lines are parallel.

### Given:
- One interior angle is \( 50^\circ \),
- The other interior angle is \( 130^\circ \).

### Sum of the angles:
\[
50^\circ + 130^\circ = 180^\circ
\]

Since the sum of these two consecutive interior angles is \( 180^\circ \), by the Converse of the Consecutive Interior Angles Theorem, lines \( l \) and \( m \) **are** parallel.

### Conclusion:
Yes, \( l \parallel m \), because the consecutive interior angles sum up to \( 180^\circ \), satisfying the condition for parallelism.

Would you like more details or further clarification? Here are some related questions:

1. What is the Converse of the Corresponding Angles Postulate?
2. Can two lines be parallel if consecutive angles do not add up to 180°?
3. What are alternate interior angles, and how do they help in proving parallelism?
4. How does the Transversal Line Theorem relate to proving parallel lines?
5. What are skew lines, and how are they different from parallel lines?

**Tip**: When dealing with parallel lines and transversals, remember that corresponding, alternate interior, and same-side interior angles are key indicators of parallelism.

Explore the conditions under which lines l and m are parallel using the Converse of the Consecutive Interior Angles Theorem. This geometry problem demonstrates the relationship between angles formed by a transversal and parallel lines, suitable for students in Grades 8-10.

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