MathNet 2009-part-03 — 175 problems (EN–VI) Question 20

In triangle $ABC$ the angle $\angle BAC = 70^\circ$ and the angle $\angle ABC = 50^\circ$. The point $M$ lies inside $\triangle ABC$ such that $\angle MAC = \angle MCA = 40^\circ$. Determine the angles $\angle AMB$ and $\angle BMC$.