I'm solving some practice problems to prepare for a competitive exam. Here is one which I'm trying to do for some time but still haven't found a solution to:
"In the given figure, $∠ABC = 2∠ACB$ and $AB = DC$. Also, $AD$ is the bisector of $∠BAC$. Find $∠ABC$."
Here is the drawing I made :
Note that I want to find the numerical value of $∠ABC$ in degrees.
Since $AB$ and $DC$ are sides of different triangle, I don't know how to begin.
Also since none of the angles is known, how can I find the value of angle?
Please help.
Hint: Let $BE$ be the bisector of $\angle ABC$ and connect $E$ with $D$. In triangles $ABE$ and $DCE$ we have $\angle ABE = \angle DCE$, $AB=DC$ and $BE=CE$. Hence $AE=ED$.