Miles said that he measured an angle of a regular polygon to be 130 degress. Explain why this result is impossible.

Answer 1

For a regular n-gon, the sum of the interior angles is
180(n-2)
so each angle is 180(n-2)/n
to have 180(n-2)/n =130
180n - 360 = 130n
50n = 360
n = 7.2

but n has to be a whole number, can't have a partial side.

so the situation is not possible