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

Explanation:

Supplementary angles sum to 180°. Exterior angles lie outside parallel lines cut by a transversal. ∠H (on PQ, outside TU) and ∠E (on RS, outside TU) are same-side exterior angles, which are supplementary for parallel lines. Other options: A are vertical angles; B are adjacent interior angles; C are not exterior/supplementary. Thus, D is correct.

Answer:

D. ∠H and ∠E