Question

m∠1 =
m∠2 =
m∠3 =

Explanation:

Step1: Find the measure of $\angle3$

$\angle3$ and the $37^{\circ}$ angle are supplementary. Supplementary angles add up to $180^{\circ}$. So, $m\angle3=180 - 37=143^{\circ}$.

Step2: Find the measure of $\angle2$

$\angle2$ and the $37^{\circ}$ angle are vertical - angles. Vertical angles are equal. So, $m\angle2 = 37^{\circ}$.

Step3: Find the measure of $\angle1$

The right - angle is $90^{\circ}$. $\angle1+\angle2 = 90^{\circ}$. Since $m\angle2 = 37^{\circ}$, then $m\angle1=90 - 37 = 53^{\circ}$.

Answer:

$m\angle1 = 53^{\circ}$
$m\angle2 = 37^{\circ}$
$m\angle3 = 143^{\circ}$