All sides of the convex pentagon $ABCDE$ are of equal length, and $\angle A = \angle B = 90^{\circ}$. What is the degree measure of $\angle E$?
Since $A$ and $B$ are right angles, and $AE$ equals $BC$, and $AECB$ is a square. Since $ED$ and $CD$ are also 5, triangle $CDE$ is equilateral. Angle $E$ is therefore $90+60=150 $ $\fbox{150}$.