  We establish existence, uniqueness and higher order weighted $L_p$-Sobolev
regularity for the stochastic heat equation with zero Dirichlet boundary
condition on angular domains and on polygonal domains in $\mathbb{R}^2$. We use
a system of mixed weights consisting of appropriate powers of the distance to
the vertexes and of the distance to the boundary to measure the regularity with
respect to the space variable. In this way we can capture the influence of both
main sources for singularities: the incompatibility between noise and boundary
condition on the one hand and the singularities of the boundary on the other
hand. The range of admissible powers of the distance to the vertexes is
described in terms of the maximal interior angle and is sharp.
