Answer
$m\angle A = 80^{\circ}$
$m\angle B = 100^{\circ}$
$m\angle C = 80^{\circ}$
$m \angle D = 100^{\circ}$
Work Step by Step
The opposite angles of a parallelogram have equal measures.
We can find the value of $x$:
$m \angle A = m \angle C$
$\frac{2x}{3} = \frac{x}{2}+20$
$\frac{2x}{3} - \frac{x}{2} = 20$
$\frac{4x}{6} - \frac{3x}{6} = 20$
$\frac{x}{6} = 20$
$x = 120$
We can find the measure of $\angle A$:
$m \angle A = \frac{2x}{3} = \frac{(2)(120)}{3} = 80^{\circ}$
We can find the measure of $\angle C$:
$m \angle C = \frac{x}{2}+20 = \frac{(120)}{2}+20 = 80^{\circ}$
Let $a = m\angle B = m \angle D$
The sum of the four angles in a parallelogram is $360^{\circ}$
We can find the value of $a$:
$80^{\circ}+a+80^{\circ}+a = 360^{\circ}$
$2a+160^{\circ} = 360^{\circ}$
$2a = 360^{\circ}-160^{\circ}$
$2a = 200^{\circ}$
$a = 100^{\circ}$
Then: $m\angle B = m \angle D = 100^{\circ}$
