# A geometric problem, calculate the angle

What is the degree of $\angle AFC$?

I have tried this, but it seems do not work

We know that $\widehat{CAB}=\widehat{CAF}+\widehat{FAB}=80^\circ$ and by Trig Ceva's theorem $$\frac{\sin\widehat{CAF}}{\sin\widehat{FAB}}\cdot\frac{\sin 10^\circ}{\sin 20^\circ}\cdot\frac{\sin 30^\circ}{\sin 40^\circ}=1\tag{1}$$ holds. $\widehat{CAF}=60^\circ$ and $\widehat{FAB}=20^\circ$ meet every constraint, hence $$\widehat{CFA}=\color{red}{80^\circ}.\tag{2}$$