SOLUTION: In a parallelogram, each of the two larger angles is twenty more than three times the smaller angles. Find the measure of each angle. What is the proper statement and solution to

Question 957602: In a parallelogram, each of the two larger angles is twenty more than three times the smaller angles. Find the measure of each angle. What is the proper statement and solution to the equation?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the opposite angles of a parallelogram are equal.
the adjacent angles of a parallelogram are supplementar6y.
the sum of the angles of a parallelogram is 360 degrees.
each of the larger angles are supplementary to each of the smaller angles.
one smaller angle plus one larger angle is equal to 180 degrees.

let x = larger angle.
let y = smaller angle.

x = 3*y + 20

x + y = 180

y = 180 - x

x = 3 * y + 20 becomes:

x = 3 * (180 - x) + 20 which becomes:

x = 3 * 180 - 3 * x + 20 which becomes:

x = 540 - 3 * x + 20 which becomes:

x = 560 - 3 * x which becomes:

4 * x = 560 which becomes:

x = 140

since x + y = 180, this means that y = 40

your larger angle is 140
your smaller angle is 40

3 * 40 + 20 = 140

solution is confirmed.

x = 140 = larger angle
y = 40 = smaller angle.

2 larger angles plus 2 smaller angles = 360 = sum of the interior angles of a parallelogram.

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