Question

which of these is sufficient to show that lines n and p are parallel? a. ∠5≅∠16 b. ∠2≅∠4 c. ∠2≅∠7 d. ∠5≅∠8

Explanation:

Step1: Recall parallel - line postulates

If corresponding angles are congruent, then the lines are parallel.

Step2: Analyze option A

∠5 and ∠16 are corresponding angles. If ∠5≅∠16, by the corresponding - angles postulate, lines n and p are parallel.

Step3: Analyze option B

∠2 and ∠4 are vertical angles. Vertical - angle congruence does not prove lines n and p are parallel.

Step4: Analyze option C

∠2 and ∠7 are neither corresponding, alternate interior, nor alternate exterior angles. Their congruence does not prove lines n and p are parallel.

Step5: Analyze option D

∠5 and ∠8 are vertical angles. Vertical - angle congruence does not prove lines n and p are parallel.

Answer:

A. ∠5≅∠16