Is it possible to have a regular polygon each of whose interior angles is 100°?

No, since is not a whole number

Sum of Interior Angle and Exterior Angle = 180°

Interior Angle = 100°

So, Exterior Angle = 180° - 100°

= 80°

No. of Sides = 360° / Exterior Angle

= 360/80

= 4.5

4.5 is not an integer. So, it is not possible to have a regular polygon whose interior angle is 100°.