Question

ente, m∠4 = 46°. hallar m∠1, m∠2 y m∠3.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles. Since $m\angle4 = 46^{\circ}$, then $m\angle1=46^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle2 = 180^{\circ}-m\angle1$. Substituting $m\angle1 = 46^{\circ}$, we get $m\angle2=180 - 46=134^{\circ}$.

Step3: Use vertical - angle property again

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3=m\angle2 = 134^{\circ}$.

Answer:

$m\angle1 = 46^{\circ}$
$m\angle2 = 134^{\circ}$
$m\angle3 = 134^{\circ}$