Question 88
For a fixed triangle $A B C$ we choose a point $M$ on the ray $C A$ (after $A$), a point $N$ on the ray $A B$ (after $B$), and a point $P$ on the ray $B C$ (after $C$) in a way such that $A M - B C = B N - A C = C P - A B$. Prove that the angles of triangle $M N P$ do not depend on the choice of $M, N, P$.