  Let $M$ be an arbitrary subset in $\mathbb R^n$ with a conic (or positive)
hull $C$. Consider its Gaussian image $AM$, where $A$ is a $k\times n$-matrix
whose entries are independent standard Gaussian random variables. We show that
the probability that the convex hull of $AM$ contains the origin in its
interior coincides with the $k$-th Grassmann angle of $C$. Also, we prove that
the expected Grassmann angles of $AC$ coincide with the corresponding Grassmann
angles of $C$. Using the latter result, we show that the expected sum of $j$-th
Grassmann angles at $\ell$-dimensional faces of a Gaussian simplex equals the
analogous angle-sum for the regular simplex of the same dimension.
