Question

given r || s and p || q
which is a true statement?
a ∠1 and ∠5 are supplementary as alternate exterior angles
b ∠3 and ∠9 are supplementary as a linear pair
c ∠11 and ∠16 are supplementary as a linear pair
d ∠10 and ∠18 are supplementary as corresponding angles

Explanation:

Step1: Recall linear - pair property

A linear - pair of angles are adjacent and supplementary, i.e., their sum is 180°.

Step2: Analyze each option

• Option A: Alternate exterior angles are congruent, not supplementary. So, ∠1 and ∠5 are not supplementary as alternate exterior angles.
• Option B: ∠3 and ∠9 are not adjacent, so they are not a linear - pair.
• Option C: ∠11 and ∠16 are adjacent angles that form a straight - line. By the definition of a linear - pair, they are supplementary.
• Option D: Corresponding angles are congruent, not supplementary. So, ∠10 and ∠18 are not supplementary as corresponding angles.

Answer:

C. ∠11 and ∠16 are supplementary as a linear pair