MathNet 2010 — Part 05 Question 66

On the exterior of a non-equilateral triangle $ABC$ consider the similar triangles (in this order) $ABM$, $BCN$ and $CAP$, such that the triangle $MNP$ is equilateral. Find the angles of the triangles $ABM$, $BCN$ and $CAP$.

Nicolae Bourbăcuţ