Question

in the figure below, m∠1 = 137°. find m∠2, m∠3, and m∠4.

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle2=180 - m\angle1$.
$m\angle2 = 180-137=43^{\circ}$

Step2: Use vertical - angle property

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are equal. So $m\angle3=m\angle1 = 137^{\circ}$

Step3: Use vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are equal. So $m\angle4=m\angle2 = 43^{\circ}$

Answer:

$m\angle2 = 43^{\circ}$
$m\angle3 = 137^{\circ}$
$m\angle4 = 43^{\circ}$