Question

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

Answer 1

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°`

Answer 2

`360^@`

Explanation:

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