Find k = ?

The exterior angle at the top vertex is $130^\circ$. The interior angle, let's call it $\alpha$, is supplementary to this exterior angle.

The double hash marks on the right side and the bottom side indicate that these two sides are equal. In an isosceles triangle, the angles opposite the equal sides are also equal. The angle opposite the right side is the bottom-left interior angle (let's call it $\beta$), and the angle opposite the bottom side is the top interior angle ($\alpha$).
Therefore, $\beta = \alpha = 50^\circ$.

The sum of the interior angles in a triangle is $180^\circ$. Let the bottom-right interior angle be $\gamma$.

The exterior angle at the bottom-right vertex is $5k$, and it is supplementary to the interior angle $\gamma$.

The value of $k$ is $\boxed{20}$.