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˚.