Prove that for each natural number $k$ there exists a natural number $n(k)$, such that for each $m\geq n(k)$ and each set $M$ of $m$ points in the plane, there can be chosen $k$ triangles, so that each has an angle greater than $120^\circ$.
Problem
Source: IV International Festival of Young Mathematicians Sozopol 2013, Theme for 10-12 grade
Tags: geometry, combinatorics, ramsey number