Given: △ABC and DE ǁ AB

Prove: ∠A + ∠ACB + ∠B = 180

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∠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