19.19 The interior angles of a convex $n$-sided polygon are denoted as $A, B, C, \cdots$, and
$$
\lg \sin A+\lg \sin B+\lg \sin C+\cdots=0 .
$$

Then the polygon is
(A) an isosceles trapezoid.
(B) a rectangle.
(C) a right triangle.
(D) a regular hexagon. (Anhui Province, Anqing and other counties and cities Junior High School Mathematics Competition, 1991)
[Solution] Given $\lg (\sin A \sin B \sin C \cdots)=0$,
$$
\begin{array}{cc}
\therefore & \sin A \sin B \sin C \cdots=1, \\
\because & 0<A, B, C, \cdots<\pi \text {, then } 0<\sin A, \sin B, \sin C, \cdots \leqslant 1 \text {, }
\end{array}
$$

Therefore, $\sin A=\sin B=\sin C=\cdots=1$,
i.e., $\square$
$$
A=B=C=\cdots=90^{\circ} \text {. }
$$
$\because$ The sum of the exterior angles of a convex $n$-sided polygon is $360^{\circ}$,
$\therefore n=360^{\circ} \div 90^{\circ}=4$. Thus, the polygon is a rectangle.
Therefore, the answer is $(B)$.