Closeness to spheres of hypersurfaces with normal curvature bounded below

For a Riemannian manifold $M^{n+1}$ and a compact domain $\Omega \subset M^{n+1}$boundedbyahypersurface$\partial \Omega$ with normal curvature bounded below, estimates are obtained in terms of the distance from $O$ to $\mathrm{\partial }\mathrm{\Omega }$ for the angle between the geodesic line joining a fixed interior point $O$ in $\mathrm{\Omega }$ to a point on $\mathrm{\partial }\mathrm{\Omega }$ and the outward normal to the surface. Estimates for the width of a spherical shell containing such a hypersurface are also presented.