The proton NMR spectra of biphenyl dissolved in two nematic liquid-crystalline solvents have been analysed to yield 12 independent dipolar coupling constants, Dij. The Dij have been used to obtain the probability distribution, Pnem(ϕ), for the angle ϕ between the ring normals. Two methods of relating Dij to Pnem(ϕ) have been used: the ME method, which invokes the maximum-entropy principle, and the AP method, which is based on the construction of a potential of mean torque from an addition of contributions from the rigid subunits in a molecule. The value of ϕ when Pnem(ϕ) is a maximum is found to be essentially independent of the solvent, and is determined to be 34 ± 1° by the ME method, and 37.2 ± 0.1° by the AP method.