19・16 Let the sum of the interior angles of polygon $P$ be $S$. It is known that each interior angle is $7 \frac{1}{2}$ times its corresponding exterior angle, then
(A) $S=2660^{\circ}$, and $P$ could be a regular polygon.
(B) $S=2660^{\circ}$, and $P$ is not a regular polygon.
(C) $S=2700^{\circ}$, and $P$ is a regular polygon.
(D) $S=2700^{\circ}$, and $P$ is not a regular polygon.
(E) $S=2700^{\circ}$, and $P$ could be a regular polygon or not a regular polygon.
(11th American High School Mathematics Examination, 1960)
［Solution］From the given and the formula for the interior and exterior angles of a polygon, we have $\frac{(n-2) \cdot 180^{\circ}}{n}=7 \frac{1}{2} \cdot \frac{360^{\circ}}{n}$, which gives $n=17$. Then $S=(17-2) \cdot 180^{\circ}=2700^{\circ}$. However, $P$ is not necessarily a regular polygon. Therefore, the answer is $(E)$.