Given: angle 1 and angle 2 are supplementary, and angle 2 and angle 3 are supplementary. Prove: angle 1= angle 3

By definition of supplementary angles, m angle 1+ m angle 2=(a) and m angle 2+ m angle 3=(b). Then, m angle 1+ m angle 2=m angle 2 + m angle 3 by the (c).
Subtract m angle 2 from each side. You get m angle 1=(d), or angle 1=(e).