Question

Lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase right angle is 110 degrees. At the intersection of lines b and e, the uppercase right angle is 110 degrees. At the intersection of lines b and f, the bottom right angle is 80 degrees.
Which lines are parallel? Justify your answer.

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

Answer 1

Lines a and b are parallel because their corresponding angles are congruent.

Justification: Line e is a transversal of lines a and b. The corresponding angles at the intersections a∩e and b∩e are both 110°, so by the converse of the Corresponding Angles Postulate the lines a and b are parallel. (The options about e and f are false because the angles at b∩e and b∩f are 110° and 80°, not supplementary or equal.)