Question

Lines b and a are intersected by line f. At the intersection of lines f and b, the bottom left angle is angle 4 and the bottom right angle is angle 3. At the intersection of lines f and a, the uppercase right angle is angle 1 and the bottom left angle is angle 2.
Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f?

m∠4 = 110° and m∠3 = 70°
m∠1 = 110° and m∠2 = 110°
m∠1 = 110° and m∠3 = 70°
m∠2 = 110° and m∠3 = 110°

Answer 1

m∠1 = 110° and m∠3 = 70°.

Reason: ∠1 and ∠2 are vertical angles, so ∠2 = 110°. ∠2 and ∠3 are consecutive interior angles on the same side of the transversal, and 110° + 70° = 180°, so they are supplementary. Consecutive interior angles supplementary implies lines a and b are parallel.