Answer
$m \angle 1 = 65^{\circ}$
$m \angle 2 = 65^{\circ}$
Work Step by Step
If the lines are parallel and are cut by a transversal, then alternate interior angles are congruent. This means that $\angle 2$ and the angle whose measure is given are alternate interior angles; therefore, $m \angle 2 = 65^{\circ}$.
$\angle 1$ is congruent to $\angle 2$ because they are vertical angles, and vertical angles are congruent; therefore, $m \angle 1$ and $m \angle 2$ are both $65^{\circ}$.
