Question

in the figure below, m∠3 = 36°. 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 $m\angle3 = 36^{\circ}$, so $m\angle1=36^{\circ}$.

Step3: Find $m\angle2$

$\angle1$ and $\angle2$ are supplementary (they form a straight - line, so $m\angle1 + m\angle2=180^{\circ}$). Then $m\angle2 = 180^{\circ}-m\angle1$. Substituting $m\angle1 = 36^{\circ}$, we get $m\angle2=180 - 36=144^{\circ}$.

Step4: Find $m\angle4$

Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4 = m\angle2$. So $m\angle4 = 144^{\circ}$.

Answer:

$m\angle1 = 36^{\circ}$
$m\angle2 = 144^{\circ}$
$m\angle4 = 144^{\circ}$