Finding the length of a side of a quadrilateral given 2 sides and two angles

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In the quadrilateral $ABCD$, $AD$ is parallel to $BC$, $\angle C = 2\angle A$, $CD=3$, and $BC=2$, What is $AD$?

I think I have to making a line bisecting $AC$, but I am not sure.

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1 Answer

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Let $CE$ (here $E \in AD$) be the bisector of $\angle C$. Then $AD = AE+ED = BC + CD$.

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