Question 1059474: In two regular polygons the difference between exterior angles is 21 degrees and the number of difference between sides is 14. Find the number of sides of each polygon?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! All the exterior angles add to 360 degrees
Therefore, if one polygon's exterior angle is x, and the other ix x-21, we have 360/x and 360/(x-21) as the number of sides
(360/x)=number of sides with the polygon with fewer sides
360/(x-21)=number of sides with the polygon with more sides. The denominator is smaller so the value is greater. For example, if x=24, one polygon would have 15 sides and the other would have 120
(360/x)+14=360/(x-21)
Multiply everything by x(x-21)
360(x-21)+14x^2-294x=360x
360x-7560+14x^2-294x=360x
14x^2-294x-7560=0
divide by 14, since all are evenly divisible
x^2-21x-540=0
(x-36)(x+15)=0
x=36 as only reasonable root.
One polygon has 36 sides and an exterior angle of 360/36=10 degrees.
The other polygon has 15 sides and an exterior angle of 360/15=24 degrees. That difference is 14 degrees.
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