Question

Horizontal and parallel lines c and d are cut by transversal p. At the intersection of lines c and p, the uppercase left angle is angle 1 and the uppercase right angle is angle 2. At the intersection of lines d and p, the uppercase right angle is angle 3 and the bottom left angle is angle 4.
Which set of equations is enough information to prove that lines c and d are parallel lines cut by transversal p?

m∠1 = 81° and m∠2 = 99°
m∠3 = 99° and m∠4 = 99°
m∠2 = 99° and m∠4 = 99°
m∠4 = 81° and m∠1 = 81°

Answer 1

m∠2 = 99° and m∠4 = 99°.

Reason: ∠2 (upper right at c) and ∠4 (lower left at d) are alternate exterior angles with respect to transversal p. If a pair of alternate exterior angles are congruent, the lines are parallel (converse of the alternate exterior angles theorem).