Question

So I kind of get proofing but I am lost for what you call it when two sides that aren't adjacent are supplementary. Is it just supplementary angles? I want to say either <3 and <1 are congruent or <2 and <3 are congruent. If I could get help on the rest of the problem that would be much appreciated.

Answer 1

Let angle 4 denote the angle adjacent to angle 3 on the right side (so between lines a and b, to the right of line c). Angles 3 and 4 are then supplementary.

Lines a and b are parallel, so angles 1 and 4 are congruent because they are alternating interior angles.

By the transitive property, angles 2 and 4 are also congruent.

Again, transitively, angles 2 and 3 are supplementary.

Let angle 5 denote the angle to the left of angle 2 (between a and b, to the left of d). Angles 5 and 2 are supplementary.

Transitively, angles 5 and 3 are congruent.

These two angles correspond to one another, so lines c and d are parallel.