Question

la figura siguiente, m∠4 = 71°. hallar m∠1, m∠2 y m∠3.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles, so $m\angle1 = m\angle4$.
$m\angle1=71^{\circ}$

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle1 + m\angle2=180^{\circ}$. Then $m\angle2 = 180^{\circ}-m\angle1$.
$m\angle2=180 - 71=109^{\circ}$

Step3: Use vertical - angle property again

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3 = m\angle2$.
$m\angle3 = 109^{\circ}$

Answer:

$m\angle1 = 71^{\circ}$
$m\angle2 = 109^{\circ}$
$m\angle3 = 109^{\circ}$