Question 966906: the ratio of the interior angle of the exterior angle of a regular polygon is 5:2.find the number of sides of the polygon.google.com
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the exterior angle of a regular polygon is equal to 360 / n, where nis the number of sides.
the interior angle of a regular polygon is equal to 180 - 360 / n, where n is the number of sides.
the ratio of the interior angle of the polygon to the exterior angle of the polygon is equual to 5/2.
thie means that (180 - 360 / n) / (360 / n) is equal to 5 / 2.
take the cross product to get:
5 * (360 / n) is equal to 2 * (180 - 360 / n)
solve for n to get n = 7.
when n = 7, the exereior angle is 360 / 7 = 51.42857143 degrees.
when n = 7, the interior angle is 180 - 51.42857143 degrees which is equal to 128.5714286 degrees.
the ratio of the interior angle to the exterior angle is equal to 128.5714286 / 51.42857143 which is equal to 2.5.
Multiply the numerator and denominator of 2.5 / 1 to get 5 / 2.
the solution is confirmed as good.
another calculation for the interioa angle would be (n-2) * 180 / n.
when n = 7, that becomes 5 * 180 / 7 which becomes 128.5714286.
the interior angle can be calculated in both ways.
it's the same either way.
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