There is no polygon having interior angles whose measures total 500 degrees.
Explanation:The sum of the interior angles of a polygon with n sides is equal to 180∘×(n−2).
So, If there is a polygon whose interior angles total 500 degrees, then
180∘×(n−2)=500
∴n−2=500∘180∘=2.78
∴n=4.78
Since n is not a whole number, there is no such polygon whose interior angles total 500 degrees.
