Answer
$m \angle A = 63^{\circ}$
$m \angle B = 117^{\circ}$
$m \angle C = 63^{\circ}$
$m \angle D = 117^{\circ}$
Work Step by Step
The opposite angles of a parallelogram have equal measures.
We can find the value of $x$:
$m \angle A = m \angle C$
$2x+3 = 3x-27$
$x = 30$
We can find the measure of $\angle A$:
$m \angle A = 2x+3 = (2)(30)+3 = 63^{\circ}$
We can find the measure of $\angle C$:
$m \angle C = 3x-27 = (3)(30)-27 = 63^{\circ}$
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 $a$:
$63^{\circ}+a+63^{\circ}+a = 360^{\circ}$
$2a+126^{\circ} = 360^{\circ}$
$2a = 360^{\circ}-126^{\circ}$
$2a = 234^{\circ}$
$a = 117^{\circ}$
Then: $m\angle B = m \angle D = 117^{\circ}$
