SOLUTION: One third of a polygon's interior angles are 150�, another third are 140� and the others are 160�. Find the number of sides in the polygon.

Question 1109017: One third of a polygon's interior angles are 150�, another third are 140� and the others are 160�. Find the number of sides in the polygon.
Found 3 solutions by Alan3354, Boreal, greenestamps:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
One third of a polygon's interior angles are 150�, another third are 140� and the others are 160�. Find the number of sides in the polygon.
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One third of a polygon's exterior angles are 30�, another third are 40� and the others are 20�. Find the number of sides in the polygon.
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n = # of sides
(n/3)*30 + (n/3)*40 + (n/3)*20 = 360
10n + 20n = 360
n = 12 sides

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
sum of angles is (n-2)(180)
x= number of angles that are 150, 140, and 160
150x+140x+160x=(n-2)180 and here n=3x
450x=(3x-2)(180)
2.5x=3x-2
0.5x=2
x=4
12 sided polygon
(n-2)(180)=1800 degrees sum of interior angles
150*4=600
140*4=560
160*4=640
add to 1800 degrees

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

There are three interior angles each of 140, 150, and 160 degrees, so the average is 150 degrees.
That means the average exterior angle is 30 degrees.
That means the number of sides is 360/30 = 12.
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