What is the largest number of acute angles that a convex hexagon can have?
$\textbf{(A)}\  2 \qquad \textbf{(B)}\  3 \qquad \textbf{(C)}\  4\qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\  6$
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 $\boxed{(B) 3}$