AMC 8 2016 Problem 23

Two congruent circles centered at points $A$ and $B$ each pass through the other circle's center. The line containing both $A$ and $B$ is extended to intersect the circles at points $C$ and $D$. The circles intersect at two points, one of which is $E$. What is the degree measure of $\angle CED$? $\textbf{(A) }90 \textbf{(B) }105 \textbf{(C) }120 \textbf{(D) }135 \textbf{(E) }150$