Can the sum of interior angles of a polygon be 4300 degree Justify?

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1076248

2026-03-29 06:45

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No, it cannot.

Consider a polygon which has n vertices, where n is an integer greater than or equal to 3.


The sum of the interior angles of such a polygon is 180*(n - 2) degrees.

Since n is an integer, (n - 2) must be an integer and so 180 must be a factor of the sum of the angles.


180 does not divide 4300 and so it cannot be the sum of interior angles.


It is, of course possible for a polygonal shape on a curved surface to have an angle sum of 4300 degrees, but such a shape would not be a polygon.




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