Question

Lines l and m are horizontal and are intersected by lines p and q. At the intersection of lines l and p, the uppercase left angle is 130 degrees. At the intersection of lines q and l, the bottom right angle is 130 degrees. At the intersection of lines m and q, the uppercase right angle is 80 degrees.
Which lines are parallel? Justify your answer.

Lines p and q are parallel because same side interior angles are congruent.
Lines p and q are parallel because alternate exterior angles are congruent
Lines l and m are parallel because same side interior angles are supplementary
Lines l and m are parallel because alternate interior angles are supplementary.

Answer 1

Lines p and q are parallel because alternate exterior angles are congruent.

Justification: Using l as a transversal of p and q, the upper-left angle at the intersection of l and p is 130° and the bottom-right angle at the intersection of l and q is also 130°. Those two angles are alternate exterior angles with respect to p and q. Since alternate exterior angles are congruent, p ∥ q. (Note: l and m are not parallel here because the interior same-side angles formed by transversal q are 130° and 80°, which are not supplementary.)