∠A = ∠ACD and ∠B = ∠BCE

Substitution

∠A + ∠ACB + ∠B = 180

Angle addition theorem

Parallel lines form equal alternate interior angles

∠DCB + ∠BCE = 180

Substitution

∠ACD + ∠ACB + ∠BCE = 180

△ABC and DE ǁ AB

∠ACD + ∠ACB = ∠DCB

Given

The angles in a linear pair are supplementary