Question

applying angle pair relationships. what is m∠2? what is m∠1?

Explanation:

Step1: Identify angle - pair relationship

$\angle 2$ and the $75^{\circ}$ angle are corresponding angles. Corresponding angles formed by parallel lines are congruent.
So, $m\angle 2 = 75^{\circ}$

Step2: Find $m\angle 1$

$\angle 1$ and $\angle 2$ are a linear - pair. A linear - pair of angles is supplementary (their sum is $180^{\circ}$).
Let $m\angle 1=x$. Then $x + m\angle 2=180^{\circ}$. Since $m\angle 2 = 75^{\circ}$, we have $x=180 - 75$.
$m\angle 1=105^{\circ}$

Answer:

$m\angle 2 = 75^{\circ}$
$m\angle 1 = 105^{\circ}$