$19 \cdot 20$ A convex $n$-sided polygon has its $n$ interior angles forming an arithmetic sequence. If the common difference is $5^{\circ}$ and the largest angle is $160^{\circ}$, then $n$ equals
(A) 9.
(B) 10.
(C) 12.
(D) 16.
(E) 32.
(19th American High School Mathematics Examination, 1968)
［Solution］Suppose the $n$ interior angles of the convex $n$-sided polygon are
$$
160^{\circ}, 160^{\circ}-5^{\circ}, 160^{\circ}-2 \cdot 5^{\circ}, \cdots, 160^{\circ}-(n-1) 5^{\circ} \text {, }
$$

Their sum is
$$
n \cdot 160^{\circ}-[1+2+\cdots+(n-1)] \cdot 5^{\circ}=\frac{5^{\circ} \cdot n(65-n)}{2},
$$

The sum of the interior angles of a convex $n$-sided polygon is $180^{\circ} \cdot(n-2)$.
Setting them equal, simplifying yields $n^{2}+7 n-144=0$.
Solving gives $n=9$ or -16 (discard).
Thus, the answer is $(A)$.