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 sum of any two adjacent angles of a parallelogram is $180^{\circ}$
We can find the value of $x$:
$m \angle A + m \angle B = 180^{\circ}$
$\frac{2x}{5} + \frac{x}{2} = 180^{\circ}$
$\frac{4x}{10} + \frac{5x}{10} = 180^{\circ}$
$\frac{9x}{10} = 180^{\circ}$
$9x = 1800^{\circ}$
$x = 200^{\circ}$
We can find the measure of $\angle A$:
$m \angle A = \frac{2x}{5} = \frac{(2)(200^{\circ})}{5} = 80^{\circ}$
We can find the measure of $\angle B$:
$m \angle B = \frac{x}{2} = \frac{200^{\circ}}{2} = 100^{\circ}$
Opposite angles in a parallelogram have the same measure.
We can find the measure of $\angle C$:
$m \angle C = m \angle A = 80^{\circ}$
We can find the measure of $\angle D$:
$m\angle D = m \angle B = 100^{\circ}$
