Given: <DAE is a straight angle

Prove: <1 + <2 + <3 = 180

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