19.26 For a convex $n$-sided polygon, the sum of $n-1$ interior angles, except one, is $2400^{\circ}$. Then the value of $n$ is 
(A) 15.
(B) 16.
(C) 17.
(D) Cannot be determined.
(China Junior High School Mathematics Correspondence Competition, 1987)
[Solution 1] Since the sum of the interior angles of a convex $n$-sided polygon is $(n-2) \cdot 180^{\circ}$, let $x$ be the degree measure of one of the interior angles. According to the problem, we have
$$
2400^{\circ}+x=(n-2) \cdot 180^{\circ},
$$

Since the right side of the equation is a multiple of 180, then $x=120^{\circ}$, thus
$$
2520^{\circ}=(n-2) \cdot 180^{\circ},
$$

which means
$$
n-2=14 \text {, or } n=16 \text {. }
$$

Therefore, the answer is (B).
[Solution 2] $\because$ Each interior angle of a convex $n$-sided polygon is between $0^{\circ}$ and $180^{\circ}$,
$\therefore$ The sum of the $n$ interior angles is between $2400^{\circ}$ and $2580^{\circ}$.
$$
\therefore 2400^{\circ}<(n-2) \cdot 180^{\circ}<2580^{\circ} \quad(n \in N) \text {, }
$$

Then $15 \frac{1}{3}<n<16 \frac{1}{3}$, which means $n=16$. Therefore, the answer is (B).