Question

in the figure below, m∠3 = 81°. 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, $m\angle1=m\angle3 = 81^{\circ}$.

Step3: Find $m\angle2$

$\angle2$ and $\angle3$ are supplementary (form a straight - line), so $m\angle2 = 180^{\circ}-m\angle3$. Substituting $m\angle3 = 81^{\circ}$, we get $m\angle2=180 - 81=99^{\circ}$.

Step4: Find $m\angle4$

Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4=m\angle2 = 99^{\circ}$.

Answer:

$m\angle1 = 81^{\circ}$
$m\angle2 = 99^{\circ}$
$m\angle4 = 99^{\circ}$