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$ABC$ and $BCE$ are triangles. Angle $C$ is $120$ degrees, and angle $A$ has twice the measure of angle $ABC$, which in turn has twice the measure of angle $CBE$.

What is the ratio of the measure of angle $A$ to angle $E$?

A

$2:1$

B

$3:2$

C

$5:2$

D

$7:4$

E

$3:1$

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