Question 996068: The measure of angle A is 30 degrees less than twice the measure of angle B . Find the measure of each angle of the parallelogram .
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A = 2 * B - 30
in a parallelogram, opposite angles are equal.
sum of the angles in a parallelogram is 360 degrees.
this means that 2A + 2B = 360.
divide both sides of this equation by 2 to get:
A + B = 180.
if A + B = 180 and A = 2 * B - 30, then 2 * B - 30 + B = 180.
combine like terms to get 3 * B - 30 = 180.
add 30 to both sides of this equation to get 3 * B = 210.
divide both sides of this equation by 3 to get B = 70 degrees.
if B = 70 degrees, then A must be equal to 110 degrees because 2 * 70 - 30 = 110.
if your parallelogram is ABCD (points are clockwise from top left), then:
angle A = 110
angle B = 70
angle C = 110
angle D = 70
sum of the angles is 220 + 140 = 360 as it should be.
angle A = angle C because opposite angles of a parallelogram are equal.
likewise angle B = angle D.
angle A is supplementary to angle B because adjacent angles of a parallelogram are supplementary.
likewise angle B is supplementary to angle C
likewise angle C is supplementary to angle D
likewise angle D is supplementary to angle A.
|
|
|
