2. In the quadrilateral $A B C D$, it holds that $\measuredangle A B C=104^{\circ}, \measuredangle A D C=128^{\circ}$, and $A B=B C=2$. Calculate the length of the diagonal $B D$.
2. Let's describe a circle $k$ with center at $B$ and radius 2. Points $A$ and $C$ lie on this circle. In this circle, the peripheral angles over the shorter arc $\overparen{A C}$ measure $\frac{104^{\circ}}{2}=52^{\circ}$, so the peripheral angles over the longer arc $\overparen{A C}$ measure $180^{\circ}-52^{\circ}=128^{\circ}$. From this, we conclude $D \in k$, hence $B D=2$.