Question

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

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, and $\angle2$ and $\angle4$ are vertical angles.

Step2: Find $m\angle1$

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

Step3: Find $m\angle2$

$\angle1$ and $\angle2$ are a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle2=180^{\circ}-m\angle1$. Substituting $m\angle1 = 132^{\circ}$, we get $m\angle2 = 180 - 132=48^{\circ}$.

Step4: Find $m\angle4$

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

Answer:

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