Lines Cut by a Transversal Answers

What is the value of x?[___]

B: [___]

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.