Question

Lines l, m, and n lie in a plane and are cut by a transversal, t. ∠1 is supplementary to ∠2, and ∠2 is supplementary to ∠3. Which lines, if any, are parallel?

A. Lines m and n.

B. Lines M and I.

C. None.

D. All three.

Answer 1

By using the properties of supplementary angles and parallel lines, we can conclude that if angles ∠1 and ∠3 are both supplementary to angle ∠2, lines l, m, and n must be parallel to each other.

Step-by-step explanation:

To determine which lines, if any, are parallel based on the information given, we need to use the properties of supplementary angles and parallel lines. Supplementary angles are two angles whose sum is 180 degrees. If angles are formed by a transversal cutting across parallel lines, corresponding angles are equal, and alternate interior and exterior angles are supplementary.

Since ∠1 is supplementary to ∠2, and ∠2 is also supplementary to ∠3, it follows that ∠1 and ∠3 are both supplementary to ∠2. Therefore, ∠1 and ∠3 must be equal because they both sum up to 180 degrees with ∠2. According to the properties of a transversal cutting through parallel lines, this implies that lines l, m, and n are all parallel to each other. Consequently, the correct answer is All three lines are parallel.