Question

Calculate the measure of each exterior angle of a 90 sided regular polygon? Explain.

Answer 1

Each exterior angle measures to `4^o`.

Explanation:

One of the method is to consider each exterior angle as an angle of rotation of any side to a direction of the next neighboring side.

Therefore, after `90` turns by an exterior angle the side returns to its original direction.

If `phi` is a measure of an external angle, it can be expressed as
`90 phi = 360^o`,
from which follows that `phi = 4^o`