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

Question

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

Philoid · Accepted Answer

No, since  is not a whole number
Sum of Interior Angle and Exterior Angle = 180&deg;

Interior Angle = 100&deg;

So, Exterior Angle = 180&deg; - 100&deg;

= 80&deg;

No. of Sides = 360&deg; / 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&deg;.