19.21 $n$ such that the degree measure of an interior angle of a regular $n$-gon is an integer has
(A) 16.
(B) 18.
(C) 20.
(D) 22.
(E) 24.
(44th American High School Mathematics Examination, 1993)
[Solution] Since the degree of an interior angle of a regular $n$-sided polygon is
$$
\frac{(n-2) 180^{\circ}}{n}=180^{\circ}-\frac{360^{\circ}}{n} \text {, }
$$

$n$ must be a divisor of 360.
Since $360=2^{3} \cdot 3^{2} \cdot 5^{1}$, its divisors have the form $n=2^{a} 3^{b} 5^{c}$, where
$$
a=0,1,2,3, \quad b=0,1,2, \quad c=0,1 .
$$

Therefore, 360 has $4 \cdot 3 \cdot 2=24$ divisors.
Since $n \geqslant 3$, we exclude 1 and 2, so there are 22 possible values for $n$. Hence, the answer is $(D)$.