Using Properties of Parallel Lines

To find $m\angle \alpha ,$ we can use the fact that $105^{\circ }$ and $\alpha$ are alternate exterior angles. By the Alternate Exterior Angles Theorem, they are congruent. Therefore, we have that $m\angle \alpha =105^{\circ }.$

To find $m\angle \theta$ we'll use the fact that $\alpha$ and $\theta$ are a linear pair. Thus, their measures add up to $180^{\circ }.$