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