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

Question

30-05-2019
Mathematics

contestada

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

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jbiain jbiain · Answer 1 · 2019-12-20T14:34:41+01:00

Answer:

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.