Given: △ABC and DE ǁ AB

Prove: ∠A + ∠ACB + ∠B = 180

∠A = ∠ACD and ∠B = ∠BCE
Substitution
∠DCB + ∠BCE = 180
Parallel lines form equal alternate interior angles
∠A + ∠ACB + ∠B = 180
∠ACD + ∠ACB + ∠BCE = 180
Angle addition theorem
Substitution
△ABC and DE ǁ AB
∠ACD + ∠ACB = ∠DCB
Given
The angles in a linear pair are supplementary