How to find this angle? triangle

Question

Triangle Image

How do I find $\angle\,\text{BCD}$? We know that $\text{AD} =\text{BC}$.

I just don't know how to find $\angle\,\text{BCD}$. I tried using parallel line but I just can't.

Answer 1

let $$AD=x$$ and the angle $$BCD=y$$ then we get after the Theorem of sines $$\frac{\sin(100^{\circ}-y)}{\sin(80^{\circ})}=\frac{\sin(80^{\circ}-y)}{\sin(20^{\circ})}$$ can you solve this?