113 The smallest interior angle of a convex polygon is $\frac{2}{3} \pi$, and the interior angles are in arithmetic progression with a common difference of $\frac{\pi}{36}$. The number of sides of this convex polygon is
A. 9
B. 16
C. 9 or 16
D. None of the above answers is correct
113 A. According to the formula for the sum of interior angles, we know
$$
\frac{1}{2}\left[2-n \cdot \frac{2}{3} \pi+n(\pi-1) \cdot \frac{\pi}{36}\right]=(n-2) \pi,
$$

which simplifies to $n^{2}-25 n+144=0$, thus $n=9$ or $n=16$.
If $n=16$, the $n$-th interior angle $=\frac{2}{3} \pi+15 \cdot \frac{\pi}{36}>\pi$, making the polygon no longer convex. Therefore, $n=9$. The correct choice is $\mathrm{A}$.