Question

Horizontal lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase left angle is 75 degrees. At the intersection of lines b and e, the uppercase right angle is 115 degrees. At the intersection of lines a and f, the bottom right angle is 75 degrees.
Which lines are parallel? Justify your answer.

Lines a and b are parallel because their alternate exterior angles are congruent.
Lines a and b are parallel because their same side exterior angles are supplementary.
Lines e and f are parallel because their alternate exterior angles are congruent.
Lines e and f are parallel because their same side exterior angles are congruent.

Answer 1

Lines e and f are parallel because their alternate exterior angles are congruent.

Justification: Transversal a creates an upper-left angle of 75° at e and a bottom-right angle of 75° at f. Those two angles are alternate exterior angles with respect to lines e and f, so by the converse of the alternate exterior angles theorem, e ∥ f.