Question

in the figure below, $m\angle 2=41^{\circ}$. find $m\angle 1$, $m\angle 3$, and $m\angle 4$.
$m\angle 1=\square^{\circ}$
$m\angle 3=\square^{\circ}$
$m\angle 4=\square^{\circ}$

Explanation:

Step1: Find m∠1 (supplementary to ∠2)

$\angle 1 + \angle 2 = 180^\circ$
$m\angle 1 = 180^\circ - 41^\circ = 139^\circ$

Step2: Find m∠3 (vertical to ∠1)

Vertical angles are equal, so $m\angle 3 = m\angle 1 = 139^\circ$

Step3: Find m∠4 (vertical to ∠2)

Vertical angles are equal, so $m\angle 4 = m\angle 2 = 41^\circ$

Answer:

$m\angle 1 = 139^\circ$
$m\angle 3 = 139^\circ$
$m\angle 4 = 41^\circ$