As the number of sides of a polygon increases from $3$ to $n$, the sum of the exterior angles formed by extending each side in succession:
$\textbf{(A)}\ \text{Increases}\qquad\textbf{(B)}\ \text{Decreases}\qquad\textbf{(C)}\ \text{Remains constant}\qquad\textbf{(D)}\ \text{Cannot be predicted}\qquad\\ \textbf{(E)}\ \text{Becomes }(n-3)\text{ straight angles}$
By the Exterior Angles Theorem, the exterior angles of all convex polygons add up to $360^\circ,$ so the sum $\boxed{\mathrm{(C)}\text{ remains constant}.}$