Using Properties of Parallel Lines

To find $m\angle \theta ,$ we can use the fact that $142^{\circ }$ and $\theta$ are corresponding angles. By the Corresponding Angles Theorem, they are congruent. Therefore, we have that $m\angle \theta =142^{\circ }.$

There are two approaches we can take to find the measure of $m\angle 2.$

1. The $142^{\circ }$ and $\alpha$ are alternate exterior angles.
2. Angles $\theta$ and $\alpha$ are vertical angles.

Let's think about the second approach. By the Alternate Exterior Angles Theorem, the pair of angles will be congruent because the lines that are cut by the transversal are parallel. Therefore, $m\angle \alpha$ is also $142^{\circ }.$