$19 \cdot 24$ If the sum of all but one of the angles of a convex polygon is $2190^{\circ}$, then the number of sides of the polygon should be
(A) 13.
(B) 15.
(C) 17.
(D) 19.
(E) 21.
(24th American High School Mathematics Examination, 1973)
[Solution] Let $n$ be the number of sides (angles) of the known convex polygon, and $x$ be the degree of the removed angle.
Then $180(n-2)=2190+x$,
so $n-2=\frac{2190+x}{180}=12+\frac{30}{180}+\frac{x}{180}=12+1$, noting that $0^{\circ}<x<180^{\circ}$.
Thus, $x=150^{\circ}, \therefore n=15$.
Therefore, the answer is $(B)$.