Posted by Guru on Monday, February 4, 2013 at 5:36pm.
In a regular polygon,each interior angle doubles its corresponding exterior angle,find the number of side of the polygon?

Maths  Reiny, Monday, February 4, 2013 at 6:15pm
let the exterior angle be
a , b, c , d, e ....
then the interior angles are
2a , 2b, 2c, ...
we know a+b+c+.. = 360
suppose we have n sides
sum of interior angles = 180(n2)
so 2a + 2b + 2c + ... = 180(n2)
2(a+b+c+.. = 180(n2)
but a+b+c+..=360
2(360) = 180(n2)
4 = n2
n = 6
There are 6 sides
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