Answer:
The measure of an exterior angle is found by the following formula: Aˆ0B=^AB-^CD2. An interior angle has its vertex at the intersection of two lines that intersect inside a circle. The sides of the angle lie on the intersecting lines. 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 ) ⋅ 180o N .
Therefore, exterior angle of a regular polygon is 180 o − ( N − 2 ) ⋅ 180 o N = 360 o N