If two chords $AB$ and $CD$ of a circle with centre $O$ meet at an internal point $E$, then $\angle AEC$ equals—

When two chords cross inside a circle, the angle between them equals half the sum of the two arcs it intercepts. Those arcs are measured by the central angles $\angle BOD$ and $\angle AOC$, giving $\angle AEC = \tfrac{1}{2}(\angle BOD + \angle AOC)$.