Question

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

Answer 1

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.