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Use the figure shown.

If m∠3 + m∠4 = 180, which lines can you conclude are parallel?
Explain.

Based on the provided diagram and the information that \( m\angle 3 + m\angle 4 = 180^\circ \), we can conclude that the lines **\( n \)** and **\( p \)** are parallel.

### Explanation:

- Angles \( \angle 3 \) and \( \angle 4 \) are **same-side interior angles** because they lie on the same side of the transversal \( q \) and between the two lines \( n \) and \( p \).
- According to the **Same-Side Interior Angles Theorem**, if the sum of two same-side interior angles is 180°, the two lines cut by the transversal must be parallel.
  
Thus, \( n \parallel p \).

### Correct Answer:
**Option B**: Lines \( n \) and \( p \) are parallel because same-side interior angles are supplementary.

Would you like further clarification or details?

Here are 5 related questions to consider:

1. What is the difference between alternate interior angles and same-side interior angles?
2. How do you prove that two lines are parallel using angle relationships?
3. What other angle pair relationships indicate that two lines are parallel?
4. How would the relationship between angles change if lines \( n \) and \( p \) were not parallel?
5. Can parallel lines ever have non-supplementary same-side interior angles?

**Tip**: Always check the sum of angles when determining relationships between lines, especially when working with transversals.

Use the figure shown. If m∠3 + m∠4 = 180, which lines can you conclude are parallel? Explain.

Learn how to determine if lines are parallel by using the same-side interior angles theorem. In this example, angles 3 and 4 sum to 180°, indicating that lines n and p are parallel. Suitable for students in Grades 8-10.

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