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What are the constructible angles ?

Wikipidia sais:

The only angles of finite order that may be constructed starting with two points are those whose order is either a power of two, or a product of a power of two and a set of distinct Fermat primes.

I don't understand the exact meaning of this, does it say that an angle is constructible if and only if it is a power of two or a product of a power and $?$ (this part I didn't understand either)

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    @J.M. Honest mistake :) Yea, I think the set of all constructible angles should be classified.2012-04-20

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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.

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    @Belgi Yea, it's fine, and by accepting that 1 is a power of 2, we get that the constructible angles are exactly the angles whose order is a power of two times a set of distinct Fermat primes.2012-04-20