PMO National Stage Oral Phase

Solution:

Since $\triangle D E C$ is an equilateral triangle, then $|D E| = |C E|$ and each angle has a measure of $60^{\circ}$. This implies that $\angle A D E$ has measure of $30^{\circ}$. Since $|A D| = |D E|$, then $\triangle A D E$ is an isosceles triangle. Thus, $\angle D A E = \angle D E A = 75^{\circ}$. The same argument on triangle $B E C$ will give us $\angle C B E = \angle C E B = 75^{\circ}$. Thus, $\angle A E B = 150^{\circ}$.