SUM OF EXTERIOR ANGLES

The number of edges and vertices determines the sum of the corners in a polygon. In a polygon, the two different types of angles are interior angles and exterior angles. In this article, we will cover the sum of exterior angles. 

An exterior angle is one formed outside the enclosure of a polygon by one of the other sides and indeed the extension of its point of intersection. The sum of a polygon’s exterior angles is 360 degrees.

To understand it better let us take a polygon that has total sides n. And let the total sum of the given polygon exterior angle be G.

• As we know that for every polygon, its interior angle sums will always be 180° × (n-2)

• And the other thing about a polygon is that a polygon has equal sides

• So the total of every angle will come out to be 180°-n-2180°n and after doing further simplification it will give a result of 360°n

• So by using the above result we can determine the sum of exterior angles = 360°n×n=360°

• So as a result we can say that a polygon having a side of n number will have a sum of exterior angle equal to 360°

Solved examples

Question 1. For a given hexagon find the sum of its exterior angles 

Answer:

We are required to find the sum of an exterior angle of the hexagon and as we know a hexagon is a type of polygon which has 6 sides so from here we can say that our n=6

And as we derived above that the sum of n-sided polygon = 360°n.

So since our n=6 so the sum f exterior angle of hexagon =360°/6=60°

Question 2. For a given pentagon find the sum of its exterior angles 

Answer :

We are required to find the sum of an exterior angle of the pentagon and as we know a pentagon is a type of polygon that has 5 sides so from here we can say that our n=5

And as we derived above that the sum of n-sided polygon = 360°n

So since our n=5 so the sum of the exterior angle of the pentagon =360°/5=72°

Question 3. For a given octagon find the sum of its exterior angles 

Answer :

We are required to find the sum of an exterior angle of the octagon and as we know an octagon is a type of polygon that has 8 sides so from here we can say that our n=8

And as we derived above that the sum of n-sided polygon = 360°n.

So since our n=8 so the sum of the exterior angle of the octagon =360°/8=45°