Question

in the figure below, m∠1 = 104°. find m∠2, 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. Also, adjacent angles are supplementary (sum to 180°). $\angle1$ and $\angle2$ are adjacent.

Step2: Find $m\angle2$

Since $\angle1$ and $\angle2$ are adjacent and supplementary, $m\angle2 = 180^{\circ}-m\angle1$. Substitute $m\angle1 = 104^{\circ}$, so $m\angle2=180 - 104=76^{\circ}$.

Step3: Find $m\angle3$

$\angle1$ and $\angle3$ are vertical angles. So $m\angle3=m\angle1 = 104^{\circ}$.

Step4: Find $m\angle4$

$\angle2$ and $\angle4$ are vertical angles. So $m\angle4=m\angle2 = 76^{\circ}$.

Answer:

$m\angle2 = 76^{\circ}$
$m\angle3 = 104^{\circ}$
$m\angle4 = 76^{\circ}$