Level 3: Construct a line (segment) that bisects the given angle

Hint: The angle bisector is an axis of symmetry.

Solution: It is natural to construct a circle with center A and radius AB, the circle intersect the other line at E. Now, imagine the angle bisector exists, it must be an axis of symmetry that maps B to E. Therefore, the midpoint of E must lie of the angle bisector, and we are done!