Question

Given m∠6 + m∠7 = 180, which postulate or theorem justifies that ℓ || m?

a. Corresponding Angles Postulate.
b. Alternate Interior Angles Theorem.
c. Alternate Exterior Angles Theorem.
d. Converse of the Consecutive Interior Angles Theorem.

Answer 1

The Converse of the Consecutive Interior Angles Theorem justifies that line ℓ is parallel to line m.

Step-by-step explanation:

The postulate or theorem that justifies the fact that ℓ || m given m∠6 + m∠7 = 180 is the Converse of the Consecutive Interior Angles Theorem (option d).

1. According to the Converse of the Consecutive Interior Angles Theorem, if two lines are cut by a transversal and the consecutive interior angles are supplementary (add up to 180 degrees), then the lines are parallel. In this case, angles 6 and 7 are consecutive interior angles and their sum is 180 degrees, which means that the lines ℓ and m are parallel.