Question

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

Answer 1

Hint: When we draw a polygon, we see that it has many vertices and we give different names to differently shaped polygons depending on the number of sides in the polygon. When we extend the length of the side longer than the vertex at the corner of the polygon, the angle between the extended side and the side next to the extended side is called the exterior angle and the angle between adjacent sides of the polygon is called the interior angle.

Complete step-by-step answer:
In the given question, we will find out the measure of each exterior angle by using the above-mentioned information.
If we start moving from one vertex to another of the polygon in the clockwise direction, we reach back to the same vertex after completing a full turn, the full turn is measured as 360 degrees. Thus, the sum of all the exterior angles present in the polygon is equal to 360 degrees.
For a regular polygon, the measure of each exterior angle will be equal to $ \dfrac{360}{n} $ degrees.
For an irregular polygon, the measure of each exterior angle is equal to the adjacent interior angle subtracted from 180 degrees.
So, the correct answer is “ $ \dfrac{360}{n} $ degrees.”.

Note: A polygon whose all the sides are equal in length is called an irregular polygon, so each angle of the regular polygon is equal and thus can be found out by the formula $ \dfrac{360}{n} $ . A polynomial whose sides are not equal to each other is called an irregular polygon. The interior angle and exterior angle are adjacent to each other; they both lie on the same line in the same plane so their summation is equal to 180 degrees. Using this approach, we can find out the exterior angle of an irregular polygon.