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Is it possible to have a polygon whose sum of the interior angles is 850 degrees

1 Answer

5 votes

Answer: No

Explanation:

The sum of the interior angles of a polygon with n sides is given by
180(n-2). Setting this equal to 850 degrees,


180(n-2)=850\\\\n-2=(85)/(18)\\\\n=(121)/(18)

Since this gives n to be a non-integer value, this is an impossible situation since a polygon must have an integer number of side lengths.