Question

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 $\ell$ and $m$ with a transversal.

Step2: Apply parallel - line theorem

The same - side interior angles postulate states that if two lines are cut by a transversal and the same - side interior angles are supplementary (sum to 180°), then the two lines are parallel. Since $m\angle3 + m\angle4=180$, lines $\ell$ and $m$ are parallel.

Answer:

C. Lines $\ell$ and $m$ are parallel because same - side interior angles are supplementary.