Question

The sum of the measures of the angles of the parallelogram is 360 degrees. In the parallelogram angles A and D have the same measure as well as angles C and B. If the measure of angle C is four times the measure of angle A find the measure of each angle

Answer 1

A and D have the same measure, let's call that x
C and B have the same measure, let's call that y
That would mean 2x+2y=360
Since C is equal to 4 times A, that means y=4x
2x+2(4x)=360
2x+8x=360
10x=360
x=36
A and D both equal 36 degrees
B and C both equal 36 times 4, or 144 degrees

Answer 2

$\angle A=\angle D\\ \angle C=\angle B\\\\ 4\angle A=\angle\ C\\\\ \angle A+\angle B+\angle C+\angle D=360\\ \angle A+\angle A+4\angle A+4\angle A=360\\ 10\angle A=360\ \ |Divide\ by\ 10\\ \angle A=36^{\circ}\\\\ \angle D=36^{\circ}\\\\ \angle B=144^{\circ}\\\\\angle C=144^{\circ}$