Question

Given: j || k

Prove: ∠ 1 and ∠ 7 are supplementary.
A) ∠ 1 and ∠ 7 are not supplementary.
B) ∠ 1 and ∠ 7 are complementary.
C) ∠ 1 and ∠ 7 form a straight angle.
D) ∠ 1 and ∠ 7 are congruent.

Answer 1

When two lines are parallel, any pair of corresponding angles formed by a transversal are congruent. Therefore, ∠1 and ∠7 are congruent.

Step-by-step explanation:

Given that j || k, we can conclude that the lines j and k are parallel. When two lines are parallel, any pair of corresponding angles formed by a transversal are congruent. Therefore, if ∠1 and ∠7 are corresponding angles, they are congruent. They do not form a straight angle (option C), nor are they complementary (option B) since complementary angles add up to 90 degrees, not 180 degrees as required for supplementary angles. Therefore, the correct answer is option D) ∠1 and ∠7 are congruent.