Question

in the figure below, m∠1 = 104°. find m∠2, m∠3, and m∠4.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, $\angle2$ and $\angle4$ are vertical angles.

Step2: Find $m\angle3$

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

Step3: Find $m\angle2$ and $m\angle4$

$\angle1$ and $\angle2$ are supplementary angles (linear - pair), so $m\angle2=180 - m\angle1$.
$m\angle2 = 180 - 104=76^{\circ}$. Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4=m\angle2 = 76^{\circ}$.

Answer:

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