A Proof of The Trapezoid Angle Theorem

A trapezoid is a quadrilateral whose two sides are parallel. In the figure below, $ABCD$ is a trapezoid and $AB$ is parallel to $CD$ . In this post, we are going to prove that in a trapezoid, the consecutive angles between a pair of parallel sides are complementary. That is, we are going to prove in the figure above that $m \angle A = m \angle D = 180$ degrees and $m \angle B + m \angle C = 180$ .