jmc

Let us call $x$ the number of sides in the polygon. The sum of all the angles of the polygon with $x$ sides is $180(x-2)$, but with the information given, it can also be expressed as $160+112(x-1)$. Therefore, setting these two equations equal: $$\begin{array}{rl}180(x-2)& =160+112(x-1)\\ 180x-360& =160+112x-112\\ 68x& =408\\ x& =6\end{array}$$ Thus, it has $\boxed{6}$ sides, and is a hexagon.