Question

in the figure below, m∠3 = 132°. find m∠1, m∠2, and m∠4.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, so $m\angle1=m\angle3$.
$m\angle1 = 132^{\circ}$

Step2: Use linear - pair property

$\angle2$ and $\angle3$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle2=180 - m\angle3$.
$m\angle2=180 - 132=48^{\circ}$

Step3: Use vertical - angle property again

$\angle2$ and $\angle4$ are vertical angles. So $m\angle4=m\angle2$.
$m\angle4 = 48^{\circ}$

Answer:

$m\angle1 = 132^{\circ}$
$m\angle2 = 48^{\circ}$
$m\angle4 = 48^{\circ}$