What is the maximum number of acute angles that can be in an $n$-sided convex polygon?
The sum of the interior and exterior angles is $180^{\circ}$, so every acute interior angle has an exterior angle greater than $90^{\circ}$. In a convex polygon, the sum of the exterior angles is $360^{\circ}$, and only three obtuse angles can fit into this. Others have shown that if at least 4 of the $n$ angles are acute, then the average of the remaining angles is greater than $180^{\circ}$, so the polygon cannot be convex. The answer is therefore 3.

Many forgot to prove that with three acute angles, a convex $n$-sided polygon can be found for every $n \geqq 3$.