Answer
$m \angle 3 = 113^{\circ}$
$m \angle 1 = 33.5^{\circ}$
$m \angle 2 = 33.5^{\circ}$
$m \angle 3 = 33.5^{\circ}$
Work Step by Step
In parallelograms, opposite angles are congruent; therefore, $m \angle 3$ is $113^{\circ}$.
In parallelograms, consecutive angles are supplementary, so $m \angle 1$, $m \angle 2$, and $m \angle 4$ are half of one of the consecutive angles. If we find the measure of a consecutive angle, we can find the measures of $\angle 1$, $\angle 2$, and $\angle 4$.
Let's find the measure of one of the consecutive angles:
$m$ consecutive angle = $180 - 113$
Subtract to solve:
$m$ consecutive angle = $67$
If we divide this consecutive angle by $2$, then we will get $m \angle 1$, $m \angle 2$, and $m \angle 4$:
$m \angle 1 = m \angle 2 = m \angle 3 = 67/2$
Divide to solve:
$m \angle 1 = m \angle 2 = m \angle 3 = 33.5^{\circ}$
