The Neumann and Young equations for three-phase contact lines, when one of the phases is a nematic liquid crystal, have been derived using momentum balances and liquid-crystal surface physics models. The Neumann equation for nematic contact lines is a balance of three tension and two bending forces, the latter arising from the characteristic anisotropic surface anchoring of nematic liquid crystal surfaces. For a given interface the bending forces are always orthogonal to the tension forces, and in the presence of a nematic phase the Neumann triangle of isotropic phases becomes the Neumann pentagon. The Young equation for solid-fluid-nematic contact lines differs from the classical equation by a bending force term, which influences the wetting regimes' transitions, the contact angles, and allows for a novel orientation-induced wetting transition cascade. For a nematic contact line, the partial wetting-spreading transition occurs for positive values of the spreading parameter, and the partial wetting-dewetting transition sets in at values smaller than the classical result. The interval of static contact angles is less than pi radians. For a given solid-nematic-isotropic fluid at a fixed temperature, the spreading --> partial wetting --> spreading --> partial wetting --> spreading transition cascade may occur when the director at the contact line rotates from the planar to the homeotropic orientation state.