The sum of the interior angles of a convex \(n\)-sided polygon is less than \(2019^\circ\). The maximum possible value of \(n\) is

The maximum is $13$. The interior angles sum to $180(n-2)^\circ$, so $n<2+\frac{2019}{180}=13+\frac{13}{60}$. Rounding the bound up gives $14$, whose angle sum is $2160^\circ$.