Question

use the figure shown. if m∠3 + m∠4 = 180, which lines can you conclude are parallel? explain
a lines n and p are parallel because alternate interior angles are congruent.
b lines n and p are parallel because same - side interior angles are supplementary.
c lines l and m are parallel because same - side interior angles are supplementary.
d lines l and m are parallel because alternate interior angles are congruent.

Explanation:

Step1: Identify angle - type relationship

$\angle3$ and $\angle4$ are same - side interior angles formed by lines $n$ and $p$ with a transversal.

Step2: Apply parallel - line theorem

The theorem states that if same - side interior angles are supplementary (sum to 180°), then the two lines are parallel. Given $m\angle3 + m\angle4=180$, lines $n$ and $p$ are parallel.

Answer:

B. Lines $n$ and $p$ are parallel because same - side interior angles are supplementary