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
a. corresponding angels theorem
b. alternate interior angels theorem
c. vertical angels theorem.
d. alternate exterior angels theorem
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
a. defenition of a linear pair
b. defenition of supplementary angels
c. linear pair postulate
d. vertical angels theorem
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.
a. congruent supplements theorem
b. defenition of a linear pair
c. defenition of supplementary angles
d. linear pair postulate