Let $X$ be a compact topological manifold with boundary. Suppose its interior is homeomorphic to $\mathbb{R}^n$. Is $X$ homeomorphic to a (closed) ball?

**Context:** I want to show that a certain compactification of moduli of convex $n$-polygons (up to scaling and rotations) is a $(2n-4)$-cell. I can degenerate all sides (but $2$, of course), keeping records of the slopes, and all angles to $\pi$ (again except $2$). If more structure is needed, like smoothness on the interior, PL at the boundary - you have it.