Are 6 degrees, 5 degrees, and 7.5 degrees constructable? So based on the theorems that I know, these angles are constructable iff the cos[itex]\vartheta[/itex] is constructible. So all that is left for me to do is show if cos[itex]\vartheta[/itex] is constructable. For 6 degrees, I tried to get a relatonship with the trig identity of cos(3[itex]\vartheta[/itex]) = 4cos3([itex]\vartheta[/itex]) - 3cos([itex]\vartheta[/itex]) because from there I could use the fact that if I can obtain a solution of the 3rd degree polynomial, then based on the rational roots theorem I could determine if the angle is constructible. My issue is, I couldn't find a simple relationship for 6degrees. I tried some higher level trig identities and "attempted" to simplify, but it started to appear futile. So now I'm at a cross roads. Same with the other two.