Question

en la siguiente, m∠2 = 108°. hallar m∠1, m∠3 y m∠4.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle2$ are supplementary (a linear - pair), and $\angle1$ and $\angle3$ are vertical angles, $\angle2$ and $\angle4$ are vertical angles.
Since $\angle1+\angle2 = 180^{\circ}$ and $\angle2 = 108^{\circ}$, then $\angle1=180^{\circ}-\angle2$.
$\angle1 = 180 - 108=72^{\circ}$

Step2: Find $\angle3$

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are congruent. So $m\angle3=m\angle1$.
$m\angle3 = 72^{\circ}$

Step3: Find $\angle4$

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are congruent. So $m\angle4=m\angle2$.
$m\angle4 = 108^{\circ}$

Answer:

$m\angle1 = 72^{\circ}$
$m\angle3 = 72^{\circ}$
$m\angle4 = 108^{\circ}$