A2. The maximum number of interior angles of an $n$-gon that can be greater than $180^{\circ}$ is:
(A) $n-1$
(B) $n-2$
(C) $n-3$
(D) $n-4$
(E) $n-5$
A2. The answer is $n-3$. From the sketch, it is clear that at most $n-3$ interior angles of an $n$-gon can be greater than $180^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_66bdf7a61d9bfcb32ca4g-10.jpg?height=343&width=203&top_left_y=1319&top_left_x=281)

The sum of the interior angles of any $n$-gon is $(n-2) \cdot 180^{\circ}$. If at least $n-2$ interior angles were greater than $180^{\circ}$, then the sum of the interior angles would be greater than $(n-2) \cdot 180^{\circ}$, which is a contradiction.