AHSME 1962 Problem 31

The ratio of the interior angles of two regular polygons with sides of unit length is $3: 2$. How many such pairs are there? $\textbf{(A)}\ 1 \textbf{(B)}\ 2 \textbf{(C)}\ 3 \textbf{(D)}\ 4 \textbf{(E)}\ \text{infinitely many}$