Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass and straightedge were sought.

Is trisecting an angle possible?

However, although there is no way to trisect an angle in general with just a compass and a straightedge, some special angles can be trisected. ... It is possible to trisect an arbitrary angle by using tools other than straightedge and compass.

Why trisecting an angle is impossible?

Since the roots have to add up to zero, this means that: ... Since the trisection equation has no constructible roots, and since cos(20°) is a root of the trisection equation, it follows that cos(20°) is not a constructible number, so trisecting a 60° angle by compass and straightedge is impossible.