Given: w ∥ x and y is a transversal. prove: ∠3 and ∠5 are supplementary. use the drop-down menus to complete the proof. given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the therefore, m∠1 = m ∠5 by the definition of congruent. we also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the by the m∠3 + m ∠1 = 180. now we can substitute m∠5 for m∠1 to get m∠3 + m∠5 = 180. therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.