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(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.

Problem Statement