2006 Pascal Problem 17

In the diagram, point E lies on line segment AB, and triangles AED and BEC are isosceles. Also, \angle DEC is twice \angle ADE. What is the size of \angle EBC?

\textbf{(A)}\ 75°\quad \textbf{(B)}\ 80°\quad \textbf{(C)}\ 60°\quad \textbf{(D)}\ 55°\quad \textbf{(E)}\ 45°

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.