The sum of the angles of two polygons is $1260^{\circ}$, and the total number of their diagonals is 14. Which are these polygons?
If the number of sides of the two polygons is $x$ and $y$, respectively, then

$$
(x-2) 180^{\circ}+(y-2) 180^{\circ}=1260^{\circ}
$$

from which

$$
y=11-x
$$

Furthermore,

$$
\frac{x(x-3)}{2}+\frac{y(y-3)}{2}=\frac{x^{2}+y^{2}-3(x+y)}{2}=14
$$

or

$$
\begin{gathered}
x^{2}+(11-x)^{2}=61 \\
x^{2}-11 x+30=0
\end{gathered}
$$

from which

$$
x_{1}=6, \quad x_{2}=5
$$

and thus

$$
y_{1}=5, \quad y_{2}=6
$$

(Jenő Silbermann, Nagyvárad.)