Trisecting the angle

Problem

Given an arbitrary angle, construct with straightedge and compass alone an angle one third as large.

Remarks

Some angles can be trisected. For example, a right angle can be trisected, because an angle of $30^\circ$ is constructible. The general problem asks for one method that works for every angle. The answer is no: the angle of $60^\circ$ cannot be trisected. The problem has solutions with other tools, such as a marked ruler or origami.

History

The problem comes from ancient Greek geometry. Pierre Wantzel proved in 1837 that it has no solution for arbitrary angles.

Explanations

L1 human

Bisecting an angle is easy with a compass. Trisecting it, that is, dividing it into three equal parts, is not possible in general with straightedge and compass alone.