Angle trisection with coefficients in the field generated by these numbers. Therefore, any number that is constructible by a sequence of steps is a root of a minimal polynomial whose degree is a power of two. Note also that radians (60 degrees, written 60°) is constructible. The argument below shows that it is impossible to construct a 20° angle. This implies that a 60° angle cannot be trisected, and thus that an arbitrary angle cannot be trisected. Denote the set of rational numbers by . If 60° could be trisected, the degree of a minimal polynomial of over would be a power
Exterior angle theorem emphasizing the failure of this statement. However, since the Euclid's exterior angle theorem is a theorem in absolute geometry it is automatically valid in hyperbolic geometry. The high school exterior angle theorem (HSEAT) says that the size of an exterior angle at a vertex of a triangle equals the sum of the sizes of the interior angles at the other two vertices of the triangle (remote interior angles). So, in the picture, the size of angle "ACD" equals the size of angle "ABC" plus the size of angle "CAB". The HSEAT is logically equivalent to the Euclidean statement that the