smc

The sum of the interior angles of a hexagon is $720$ degrees. In a convex polygon, each angle must be strictly less than $180$ degrees. Six acute angles can only sum to less than $90\cdot 6=540$ degrees, so six acute angles could not form a hexagon. Five acute angles and one obtuse angle can only sum to less than $90\cdot 5+180=630$ degrees, so these angles could not form a hexagon. Four acute angles and two obtuse angles can only sum to less than $90\cdot 4+180\cdot 2=720$ degrees. This is a strict inequality, so these angles could not form a hexagon. (The limiting figure would be four right angles and two straight angles, which would really be a square with two "extra" points on two sides to form the straight angles.) Three acute angles and three obtuse angles work. For example, if you pick three acute angles of $80$ degrees, the three obtuse angles would be $160$ degrees and give a sum of $80\cdot 3+160\cdot 3=720$ degrees, which is a genuine hexagon. Thus, the answer is $\boxed{3}$