  For a convex domain $D$ that is enclosed by the hypersurface $\partial D$ of
bounded normal curvature, we prove an angle comparison theorem for angles
between $\partial D$ and geodesic rays starting from some fixed point in $D$,
and the corresponding angles for hypersurfaces of constant normal curvature.
Also, we obtain a comparison theorem for support functions of such surfaces. As
a corollary, we present a proof of Blaschke's Rolling Theorem.
