# Lets find out sum of exterior angles of a polygon:

The sum of exterior angles of a polygon is always equal to 360° provided we take 1 exterior angles of a polygon at each vertex. From this the exterior angle of a regular polygon can be calculated by dividing 360 with number of sides of a polygon. For example, exterior angle of a regular hexagon is always equal to 360/6 = 60°. Exterior angle for a regular triangle is equal to 360/3 = 120°. Similarly exterior angle for a regular pentagon is equal to 360/5 = 72° and that for a regular octagon is 360/8 = 45°. This shows that exterior angle of regular polygon keeps on decreasing as the number of sides increases in a polygon. This formula can be applied to any convex polygon. For a concave polygon, some of the angles has to be taken negative to cope up with the formula.

## Theorem for deriving exterior angles of a polygon formula:

The polygon exterior angle sum theorem helps to find out the generalized exterior angles of a polygon formula. This theorem states that the sum of exterior angles of a convex polygon is equal to the difference between sum of angles of linear pairs and sum of interior angles of a polygon. From this theorem, Sum of exterior angles S = 180n – 180(n – 2), where n is number of sides of a polygon.

i.e. S = 180n – 180n + 360 = 360°.

The figure given above shows a Pentagon and its exterior angles. From the theorem, we have

∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 360°. This theorems helps to calculate exterior angles sum for a n-sided polygon where n is a finite number.

 Ian Roberts Engineer San Francisco, USA "If you're at school or you just deal with mathematics, you need to use Studygeek.org. This thing is really helpful." Lisa Jordan Math Teacher New-York, USA "I will recommend Studygeek to students, who have some chalenges in mathematics. This Site has bunch of great lessons and examples. " John Maloney Student, Designer Philadelphia, USA " I'm a geek, and I love this website. It really helped me during my math classes. Check it out) " Steve Karpesky Bookkeeper Vancuver, Canada "I use Studygeek.org a lot on a daily basis, helping my son with his geometry classes. Also, it has very cool math solver, which makes study process pretty fun"