Prove that if two angles are supplementary to the same angle, then they are congruent.
We'll say that ∠1 and ∠2 are both supplementary to ∠3. Our goal is to prove that ∠1 and ∠2 are congruent.
Supplementary angles are just like complementary angles, except their sum is 90°, not 180°. That means m∠1 + m∠3 = 180 and m∠2 + m∠3 = 180. Subtracting m∠3 from both sides of both equations we have both m∠1 and m∠2 equaling 180 – m∠3. If that's not congruent, we don't know what is.