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