Since it was first suggested1that a single molecule might function as an active electronic component, a number of techniques have been developed to measure the charge transport properties of single molecules2-12. Although scanning tunnelling microscopy observations under high vacuum conditions can allow stable measurements of electron transport, most measurements of a single molecule bonded in a metal-molecule-metal junction exhibit relatively large variations in conductance. As a result, even simple predictions about how molecules behave in such junctions have still not been rigorously tested. For instance, it is well known13,14that the tunnelling current passing through a molecule depends on its conformation; but although some experiments have verified this effect15-18, a comprehensive mapping of how junction conductance changes with molecular conformation is not yet available. In the simple case of a biphenyl-a molecule with two phenyl rings linked by a single C-C bond-conductance is expected to change with the relative twist angle between the two rings, with the planar conformation having the highest conductance. Here we use amine link groups to form single-molecule junctions with more reproducible current-voltage characteristics19. This allows us to extract average conductance values from thousands of individual measurements on a series of seven biphenyl molecules with different ring substitutions that alter the twist angle of the molecules. We find that the conductance for the series decreases with increasing twist angle, consistent with a cosine-squared relation predicted for transport through π-conjugated biphenyl systems13.