Question

Given: w ∥ x and y is a transversal.
Prove: ∠3 and ∠5 are supplementary.

Parallel and diagonal lines w and x are cut by horizontal transversal y. On line w where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 3, 4, 2. On line x where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 7, 8, 6.
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.

Answer 1

Given that w ∥ x and y is a transversal, we know that ∠1 ≅ ∠5 by the Corresponding Angles Postulate. 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 Linear Pair Postulate. By the definition of supplementary angles, 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.