What is the sum of the exterior angles of a polygon with 4 sides? 5 sides? 6 sides? n sides?

2 Answers
Jul 29, 2018

The sum of the exterior angles is always 360°

Explanation:

The interior angle of a polygon can be found by:

(180(n-2))/n where n is the number of sides

a) 4 sides
Interior angle is equal to:
(180(4-2))/4=90

Therefore, exterior angle is equal to 180-90=90^@

The sum = 4 xx 90° = 360°

b) 5 sides
Interior angle is equal to:
(180(5-2))/5=108

Therefore, exterior angle is equal to 180-108=72^@

The sum = 5 xx72° = 360°

c) 6 sides
Interior angle is equal to:
(180(6-2))/6=120

Therefore, exterior angle is equal to 180-120=60^@

The sum = 6 xx 60° = 360°

d) n sides
Interior angle is equal to:
(180(n-2))/n

So exterior angle is equal to 180-(180(n-2))/n which can be simplified

180-(180(n-2))/n

=(180n-(180(n-2)))/n

=(180n-180n+360)/n

exterior angle =360/n

The sum = 360/n xx n = 360°

Jul 29, 2018

360^@

Explanation:

"The sum of the exterior angles of any polygon is "360^@