Is it possible for the sum of the internal angles of a polygon to be 5400 degrees?

# Any exterior angle of a polygon corresponds to an interior angle, and their sum is 180 degrees. # If there are n sides (and therefore n vertices) then the sum of all the interior and exterior angles must be 180n. # The external angles of a polygon total 360 degrees, else it could not be a closed shape. # From the above three points, it follows that the sum of interior angles is given by 180n - 360. So, if there is an integer solution to 180n - 360 = 180(n - 2) = 5400, then the answer to your question is yes. 180(n - 2) = 5400 n - 2 = 30 n = 32 A polygon with 32 sides fulfills the criterion. That would be, hmmm, a triacontakaidigon, of course.