Question

Given angles ∠4 is parallel to ∠15 (p∥q) and ∠4 is parallel to ∠15 (r∥s), prove ∠4 is supplementary to ∠15.

A) ∠4 and ∠15 form a linear pair.
B) ∠4 and ∠15 are complementary.
C) ∠4 and ∠15 are supplementary.
D) The relationship between ∠4 and ∠15 cannot be determined from the given information.

Answer 1

To prove that ∠4 is supplementary to ∠15, we can use the transitive property of parallel lines. Corresponding angles formed by parallel lines are congruent. Therefore, ∠4 is supplementary to ∠15.

Step-by-step explanation:

To prove that ∠4 is supplementary to ∠15, we can use the transitive property of parallel lines. Since ∠4 is parallel to ∠15 in both p∥q and r∥s, we can say that ∠4 and ∠15 are corresponding angles. Corresponding angles formed by parallel lines are congruent.

Therefore, ∠4 = ∠15.

Since corresponding angles ∠4 and ∠15 are congruent, they are both supplementary to the same angle. So, ∠4 is supplementary to ∠15.