$19 \cdot 25$ The value obtained by subtracting the measure of one interior angle from the sum of the interior angles of a convex polygon is $2570^{\circ}$. The measure of this interior angle should be
(A) $90^{\circ}$.
(B) $105^{\circ}$.
(C) $120^{\circ}$.
(D) $130^{\circ}$.
(E) $144^{\circ}$.
(33rd American High School Mathematics Examination, 1982)
[Solution] The sum of the interior angles of a convex $n$-sided polygon is $(n-2) \cdot 180^{\circ}$. Suppose $x$ is the required interior angle, then we have
$(n-2) \cdot 180^{\circ}=2570^{\circ}+x$, where $0^{\circ}<x<180^{\circ}$. If $n>17$, then $x$ will exceed $180^{\circ}$, which contradicts the condition of a convex polygon.
Therefore, the answer is $(D)$.