CEMC Pascal, 2006

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, point $E$ lies on line segment $AB$ , with $\angle DAE = 70^\circ$ , and triangles $AED$ and $BEC$ are isosceles. Also, $\angle DEC$ is twice $\angle ADE$ . What is the size of $\angle EBC$ ?

(A) $75^\circ$ (B) $80^\circ$ (C) $60^\circ$ (D) $55^\circ$ (E) $45^\circ$

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