SOLUTION: My question: In a parallelogram the opposite amgles have the same measures. Each of the two larger angles in a parallelogram is 20 degrees less than 3 times the smaller angles.

Question 148247This question is from textbook
: My question: In a parallelogram the opposite amgles have the same measures. Each of the two larger angles in a parallelogram is 20 degrees less than 3 times the smaller angles. Find the measure of each angle. I am unsure how to solve this equation. Thank you for your help. This question is from textbook

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let the larger angles be A and the smaller angles be B.
You know that in any quadrilateral, the sum of the interior angles is 360 degrees, so you can write:
2A+2B = 360 Simplify this to:
A+B = 180
From the problem statement, you have that A = 3B-20, right?
Substitute this into the first equation and solve for B.
(3B-20)+B = 180
4B-20 = 180
4B = 200
B = 50 degrees.
A = 3B-20
A = 3(50)-20
A = 150-20
A = 130 degrees.
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