Given: ABCD is a parallelogram.

Prove: m∠A + m∠B + m∠C + m∠D = 360˚

Parallelogram A B C D is shown.

By the definition of a parallelogram, AD∥BC and AB∥DC. Using, AD as a transversal, ∠A and ∠are same-side interior angles, so they are . By the definition of supplementary, m∠A + m∠D = 180. Using side as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. By the definition of supplementary, m∠B + m∠C = 180. So, m∠A + m∠D + m∠B + m∠C = 180 + 180 by the property. Simplifying, we have m∠A + m∠B + m∠C + m∠D = 360˚.