Given: p || q, and r || s. prove: ∠1 and ∠14 are supplementary angles. what is the next step in the proof? choose the most logical approach. a. statement: ∠6 ≅ ∠14 reason: for parallel lines cut by a transversal, corresponding angles are congruent. b. statement: ∠6 ≅ ∠7 reason: vertical angles theorem c. statement: ∠6 and ∠5 are supplementary. reason: linear pair theorem d. statement: m∠6 + m∠8 = 180° reason: angle addition

A.

Statement: ∠6 ≅ ∠14

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

Step-by-step explanation:

In the figure attached, a plot of the problem is shown.

Given p || q and r is a transversal which cut p and q, then ∠1 ≅ ∠5 and ∠2 ≅ ∠6.

Given r || s and q is a transversal which cut r and s, then ∠6 ≅ ∠14 and ∠8 ≅ ∠16.

From the picture we see that ∠1 and ∠2 are supplementary, that is, their addition is equal to 180º. ∠2 ≅ ∠6 and ∠6 ≅ ∠14, then ∠2 ≅ ∠14, in consequence ∠1 and ∠14 are supplementary.

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step-by-step explanation: