Question

In a regular polygon,each interior angle doubles its corresponding exterior angle,find the number of side of the polygon?

Answer 1

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(n-2)

so 2a + 2b + 2c + ... = 180(n-2)
2(a+b+c+.. = 180(n-2)
but a+b+c+..=360
2(360) = 180(n-2)
4 = n-2
n = 6

There are 6 sides