Question

How do you find the measure of each exterior angle of a polygon?

Answer 1

You can find a measure of an exterior angle of a regular polygon with `N` sides.
It is equal to `360^o/N`.

Explanation:

Angles of a general polygon (exterior and interior) with more than 3 sides are not defined by the lengths of its sides.

However, we can calculate the sum of all interior or exterior angles of any convex polygon. It equals to `360^o`.

It can be proven geometrically since each exterior angle describes a rotation by some angle and a sum of all exterior angles describes a rotation by full angle of `360^o`. So, if all exterior angles are equal, like in a regular polygon, each one equals to `360^o/N`.

It can also be defined with some algebraic calculations based on the fact that a sum of all interior angles is `(N-2)*180^o`.

Dividing the above by `N` we will obtain a value of an interior angle: `[(N-2)*180^o]/N`.

Therefore, exterior angle of a regular polygon is
`180^o - [(N-2)*180^o]/N = 360^o/N`