Question

The angle which is constructible by compass must be the

Answer 1

It means an angle is constructible if and only if its order is either a power of two, or a power of two times a set of Fermat primes. For example, 10 = 2*5, and 2 is a power of two and 5 is a fermat prime, thus you can make an angle of 360/10 = 36 degrees. but 40 degrees = 360/9 cannot be constructed, because 9=3*3, and 3, 3 are not distinct.