# I'm not sure about this question... The measure of an exterior angle of a regular n-gon is 72 degrees. classify the polygon by number of sides. I think it's a heptagon but i'm not sure it might be...

I'm not sure about this question...

The measure of an exterior angle of a regular n-gon is 72 degrees. classify the polygon by number of sides.

I think it's a heptagon but i'm not sure it might be a pentagon.

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### 2 Answers

Each interior angle of n regular polygone is

(i)

since exterior angel of given polygone is

Therefore corresponding interior angle is =

substitute 108 in (i) ,we have

Polygone has 72 sides.

You did not say if it's a heptagon or pentagon.

Each interior angle of n regular polygone is

`angle s=((n-2)xx180)/n` (i)

since exterior angel of given polygone is `72^o`

`` Therefore corresponding interior angle is =`180-72=108^o`

substitute 108 in (i) ,we have

`108=((n-2)xx180)/n`

`108n=180n-360`

`360=72n`

`n=72`

Polygone has 72 sides.