Given: ∠DAE is a straight angle

Prove: ∠1 + ∠2 + ∠3 = 180

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Angle addition theorem
∠DAE is a straight angle
Substitution
∠DAC + ∠3 = ∠DAE
Definition
∠1 + ∠2 + ∠3 = ∠DAE
Angle addition theorem
Substitution
∠1 + ∠2 + ∠3 = 180
∠1 + ∠2 = ∠DAC
∠DAE = 180
Given