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

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

May 20, 2021

#1
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Well,
360 = (n - 2)180

2 = n - 2

4 = n
therefore it should be a square.
Correct me if I'm wrong.

May 20, 2021
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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
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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
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Thanks Textot, you are right.

Sorry for contradicting you Jeager.

I muddled up exterior angle with external angle. Melody  May 22, 2021
#2
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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.

May 20, 2021
edited by Melody  May 20, 2021