Never.
The equation to find the sum of the interior angles is 180(n-2) where n is the number of sides.
If there is a polygon that has 300 degrees, 180(n-2)=300 will have n as a whole number, let's see if it does.
180(n-2)=300
180n-360=300
180n=660
660/180 is 3 2/3 and is therefore not a whole number, this means that there isn't a polygon that has 300 degrees as the sum of it's interior angles.
Hope this helps :)
