How many sides has an equiangular polygon if the sum of its exterior angles is equal to the sum of its interior angles?

Guest May 20, 2021

#1**0 **

Well,

360 = (n - 2)180

2 = n - 2

4 = n

therefore it should be a square.

Correct me if I'm wrong.

Yeager May 20, 2021

#3**+1 **

Hi Yeager,

It is nice to see you trying to make a positive contribution.

the interior angles of a square add up to 90*4 = 360

the exterior angles add up to 270*4 = 1080 degrees

Melody
May 20, 2021

#4**+1 **

I believe Yeager is correct since the external angle of an equiangular polygon could be the angle that is supplementary to the interior angle.

There are 2 definitions for exterior angles, and as Melody said, one of the definitions (360 - interior angle) will make the problem have no solutions.

textot
May 21, 2021

#2**0 **

How many sides has an equiangular polygon if the sum of its exterior angles is equal to the sum of its interior angles?

MMm

I think that is impossible...

The interior angles have to be less than 180 degrees and the exterior angles have to be more than 180 degrees.

Since there is the same number of each, the exterior angles must add up to more.

Melody May 20, 2021