Question

in the figure below, m∠2 = 77°. find m∠1, m∠3, and m∠4.

Explanation:

Step1: Use vertical - angle property

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, $m\angle1 = m\angle3$. Also, $\angle1$ and $\angle2$ are supplementary (a linear - pair, so $m\angle1+m\angle2 = 180^{\circ}$). Given $m\angle2 = 77^{\circ}$, then $m\angle1=180^{\circ}-77^{\circ}=103^{\circ}$.

Step3: Find $m\angle3$

Because $\angle1$ and $\angle3$ are vertical angles, $m\angle3=m\angle1 = 103^{\circ}$.

Step4: Find $m\angle4$

Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4 = m\angle2=77^{\circ}$.

Answer:

$m\angle1 = 103^{\circ}$
$m\angle3 = 103^{\circ}$
$m\angle4 = 77^{\circ}$