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

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