If the sum of all the angles except one of a convex polygon is $2190^{\circ}$, then the number of sides of the polygon must be 
$\textbf{(A)}\ 13 \qquad \textbf{(B)}\ 15 \qquad \textbf{(C)}\ 17 \qquad \textbf{(D)}\ 19 \qquad \textbf{(E)}\ 21$
Let $n$ be the number of sides in the polygon.  The number of interior angles in the polygon is $180(n-2)$.  We know that the sum of all but one of them is $2190^{\circ}$, so the sum of all the angles is more than that.
\[180(n-2) > 2190\]
\[n-2 > 12 \tfrac{1}{6}\]
\[n > 14 \tfrac{1}{6}\]
The sum of the angles in a 15-sided polygon is $2340^{\circ}$, making the remaining angle $150^{\circ}$.  The angles of a convex polygon are all less than $180^{\circ}$, and since adding one more side means adding $180^{\circ}$ to the measure of the remaining angle, we can confirm that there are $\boxed{\textbf{(B)}\ 15}$ sides in the polygon.