Question

in the picture below, line pq is parallel to line rs, and the lines are cut by a transversal, line tu. the transversal is not perpendicular to the parallel lines.

note: figure is not drawn to scale.

which of the following are supplementary exterior angles?

a. ∠x and ∠e
b. ∠h and ∠e
c. ∠e and ∠f
d. ∠h and ∠g

Explanation:

First, identify exterior angles: ∠H (outside PQ & TU) and ∠E (outside RS & TU) are exterior angles. Since PQ || RS and TU is a transversal, consecutive exterior angles (on the same side of the transversal) are supplementary. ∠H and ∠E are consecutive exterior angles, so they add up to 180°. Other options: A (∠X is interior, ∠E exterior), C (vertical angles, equal), D (vertical angles, equal). Thus, B is correct.

Answer:

B. ∠H and ∠E