SOLUTION: Suppose parallelogram has angles defined by the following expressions: angle A = 6x + 19; angle B = 3x - 19; angle C = 6x + 19; and angle D = 3x - 19. Then the measure of the small

Algebra ->  Angles -> SOLUTION: Suppose parallelogram has angles defined by the following expressions: angle A = 6x + 19; angle B = 3x - 19; angle C = 6x + 19; and angle D = 3x - 19. Then the measure of the small      Log On


   

Question 844147: Suppose parallelogram has angles defined by the following expressions: angle A = 6x + 19; angle B = 3x - 19; angle C = 6x + 19; and angle D = 3x - 19. Then the measure of the smallest angle is _______ degrees
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We know that teachers like to measure angles in degrees, and that is why the last word of the problem is "degrees".
We know that the sum of the measures of the angles of a quadrilateral is 180%5Eo .
The teacher knows that in a parallelogram opposite angles have the same measure. That is why the teacher made A=C and B=D.
A consequence of all of the facts above is that adjacent angles are supplementary and
A%2BB=180
%286x%2B19%29%2B%283x-19%29=180
6x%2B19%2B3x-19=180
6x%2B3x%2B19-19=180
9x=180
x=180%2F9
x=20
3x-19=3%2A20-19-->3x-19=60-19-->3x-19=highlight%2841%29
Then the measure of the smallest angle is highlight%2841%29 degrees.