Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 1620, 2340, and 7560.
We use the formula for the sum of the interior angles of a polygon: $180(n-2)$, where $n$ is the number of sides of the polygon. Setting up the equations, we have \begin{align*}
180(n-2)&=1620,\\
180(n-2)&=2340,\\
180(n-2)&=7560.
\end{align*} Dividing both sides of each equation by 180, we have \begin{align*}
n-2&=9,\\
n-2&=13,\\
n-2&=42.
\end{align*} Solving each of the equations, we have $n=11$, $n=15$, and $n=44$. Thus, the possible numbers of sides of the polygon are $\boxed{11, 15, 44}$.