19.35 A regular $m$-sided polygon is exactly surrounded by $m$ regular $n$-sided polygons (without gaps or overlaps), as shown in the case when $m=4, n=8$. If $m=10$, then $n=$
(A) 5.
(B) 6.
(C) 14.
(D) 20.
(E) 26.
(45th American High School Mathematics Examination, 1994)
[Solution] According to the formula for the interior angle of a regular $n$-sided polygon, the degree of each interior angle of a regular 10-sided polygon is
$$
\frac{180^{\circ} \cdot(10-2)}{10}=144^{\circ} \text {. }
$$

According to the problem, $144^{\circ}+2 \cdot \frac{180^{\circ} \cdot(n-2)}{n}=360^{\circ}$.
Solving for $n$ yields $n=5$.
Therefore, the answer is $(A)$.