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 Quote by Gib Z No it doesn't nessicarily mean that, with regards to what mjsd just quoted you on, werg. Say n=3, one angle could be 60 + e, another 60-e, and the other 6. You can't construct e since it is transcendental.
I don't believe Werg22 meant constructible in the sense of being constructible with ruler and compass, but merely whether or not there would exist an n-sided polygon that had those n angles for its internal angles.

My thoughts on the problem are that if you can find n numbers that add to 180(n-2) then you can construct a polygon that has at least (n-2) of these same angles, I haven't proved this, but it makes some bit of sense, however I am not sure as to whether the final two angles are guaranteed to be equal to the original two numbers in your sequence, because there are an infinite number of other numbers that will sum to the remaining angle measure that must be present in the n-gon.

Edit: For example with a triangle you can arbitrarily choose one angle, and then the other two angles depend on the lengths of the sides that form the original angle, I believe it will be a similar situation for larger n.

Edit 2: Maybe you should disregard everything I just said, after a bit more thought it seems you may be able to choose arbitrarily (n-1) angles which then guarentees you the final angle to be from the initial sequence.