MathNet 2007-part-02 — 187 problems (EN–VI) Question 90

Let $M$ be an interior point of the triangle $A B C$ with angles $\varangle B A C = 70^{\circ}$ and $\varangle A B C = 80^{\circ}$. If $\varangle A C M = 10^{\circ}$ and $\varangle C B M = 20^{\circ}$, prove that $A B = M C$.