1. Inside square $A B C D$, a point $E$ is chosen so that triangle $D E C$ is equilateral. Find the measure of $\angle A E B$.
Answer: $150^{\circ}$

Solution: Since $\triangle D E C$ is an equilateral triangle, then $|D E|=|C E|$ 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, $\angle A E B=150^{\circ}$.