Answer
$m \angle A = 83^{\circ}$
$m \angle B = 97^{\circ}$
$m \angle C = 83^{\circ}$
$m\angle D = 97^{\circ}$
Work Step by Step
The sum of any two adjacent angles of a parallelogram is $180^{\circ}$
We can find the value of $x$:
$m \angle A + m \angle B = 180^{\circ}$
$(2x+3)+ (3x-23) = 180^{\circ}$
$5x-20 = 180^{\circ}$
$5x = 200^{\circ}$
$x = 40^{\circ}$
We can find the measure of $\angle A$:
$m \angle A = 2x+3 = (2)(40)+3 = 83^{\circ}$
We can find the measure of $\angle B$:
$m \angle B = 3x-23 = (3)(40)-23 = 97^{\circ}$
Opposite angles in a parallelogram have the same measure.
We can find the measure of $\angle C$:
$m \angle C = m \angle A = 83^{\circ}$
We can find the measure of $\angle D$:
$m\angle D = m \angle B = 97^{\circ}$
