ILL 1982 Problem 43

(a) What is the maximal number of acute angles in a convex polygon?(b) Consider $m$ points in the interior of a convex $n$ -gon. The $n$ -gon is partitioned into triangles whose vertices are among the $n + m$ given points (the vertices of the $n$ -gon and the given points). Each of the $m$ points in the interior is a vertex of at least one triangle. Find the number of triangles obtained.