Step-by-step explanation:
1. ∠2 and ∠5 are supplementary
This is the information that was given in the problem statement.
2. ∠3 ≅ ∠2
∠2 and ∠3 are vertical angles, and therefore congruent.
3. ∠3 and ∠5 are supplementary
By combining statements 1 and 2, we can show through substitution that ∠3 and ∠5 are supplementary.
4. l || m
∠3 and ∠5 are consecutive interior angles. By the converse of consecutive interior angles theorem, if consecutive interior angles formed by a transversal intersecting two lines are congruent, then the lines are parallel.
