  We prove a weighted $L_p$-estimate for the stochastic convolution associated
to the stochastic heat equation with zero Dirichlet boundary condition on a
planar angular domain $\mathcal{D}_{\kappa_0}\subset\mathbb{R}^2$ with angle
$\kappa_0\in(0,2\pi)$. Furthermore, we use this estimate to establish existence
and uniqueness of a solution to the corresponding equation in suitable weighted
$L_p$-Sobolev spaces. In order to capture the singular behaviour of the
solution and its derivatives at the vertex, we use powers of the distance to
the vertex as weight functions. The admissible range of weight parameters
depends explicitly on the angle $\kappa_0$.
