$\angle 2$ is supplementary to $\angle 7$ because this is given. $\angle 2$ is supplementary to $\angle 3$ because of the definition of a linear pair. Because of the Congruent Supplements Theorem, $\angle 7\cong\angle 3$. Therefore, because of the Converse of the Corresponding Angles Theorem, $l\parallel m$.
Work Step by Step
Use properties that relate the measures of the various angles shown to find a relationship that can be applied to one of the theorems that proves that the lines are parallel. Similarly, you could use known properties that show angles 3 and 6 are supplementary and then use the Converse of the Same-Side Interior Angles Postulate to prove lines l and m are parallel.