Question

in the figure below, m∠1 = 71°. find m∠2, m∠3, 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. Also, $\angle1$ and $\angle2$ are supplementary (form a straight - line, sum to 180°).

Step2: Find $m\angle2$

Since $\angle1$ and $\angle2$ are supplementary, $m\angle2=180 - m\angle1$. Given $m\angle1 = 71^{\circ}$, then $m\angle2=180 - 71=109^{\circ}$.

Step3: Find $m\angle3$

Because $\angle1$ and $\angle3$ are vertical angles, $m\angle3=m\angle1 = 71^{\circ}$.

Step4: Find $m\angle4$

Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4=m\angle2 = 109^{\circ}$.

Answer:

$m\angle2 = 109^{\circ}$
$m\angle3 = 71^{\circ}$
$m\angle4 = 109^{\circ}$