SOLUTION: Opposite angles have the same meausres. Each of the two larger angles in a parallelogram is 20degrees less than 3 times the smaller angles. Find the measure of each angle. Answer

Question 425895: Opposite angles have the same meausres. Each of the two larger angles in a parallelogram is 20degrees less than 3 times the smaller angles. Find the measure of each angle. Answer is the smaller angles are 50 and the larger angles are 130 but how do I come up with this?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = the smaller angle
3*x - 20 = the larger angle

there are 2 smaller angles and 2 larger angles in a parallelogram.

sum of all interior angles in a parallelogram is equal to 360 degrees.

formula is:
2*x + 2*(3*x-20) = 360
simplify to get:
2*x + 6*x - 40 = 360
combine like terms to get:
8*x - 40 = 360
add 40 to both sides of equation to get:
8*x = 400
divide both sides of equation by 8 to get:
x = 50 (smaller angle)
3*x - 20 = 130 (larger angle)

fyi:

formula for determining the sum of the interior angles of a polygon is:

S = (n-2)*180

S = sum of the interior angles.
n = number of sides.

in a parallelogram, there are 4 sides.
replace n with 4 to get:
S = 180*(4-2) = 180*2 = 360.

for a triangle, there are 3 sides.
replace n with 3 to get:

S = 180*(3-2) = 180*1 = 180.

works well.

here's a reference if you're interested.

http://www.freemathhelp.com/feliz-interior-polygon.html

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