Question

en la siguiente figura, m∠3 = 49°. hallar m∠1, m∠2 y m∠4.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles.
$m\angle1 = m\angle3$

Step2: Substitute the value of $\angle3$

Since $m\angle3 = 49^{\circ}$, then $m\angle1=49^{\circ}$

Step3: Use linear - pair property

$\angle2$ and $\angle3$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle2 + m\angle3=180^{\circ}$, then $m\angle2=180^{\circ}-m\angle3$

Step4: Calculate $m\angle2$

Substitute $m\angle3 = 49^{\circ}$ into the formula, $m\angle2 = 180 - 49=131^{\circ}$

Step5: Use vertical - angle property for $\angle4$

$\angle2$ and $\angle4$ are vertical angles. So $m\angle4 = m\angle2$

Step6: Get the value of $m\angle4$

Since $m\angle2 = 131^{\circ}$, then $m\angle4=131^{\circ}$

Answer:

$m\angle1 = 49^{\circ}$
$m\angle2 = 131^{\circ}$
$m\angle4 = 131^{\circ}$