In unified models of active galaxies the direct line of sight to the nucleus is unobscured only within a certain cone of directions. An opening angle for this cone is usually estimated by methods such as the overall ratio of Seyfert 1s to Seyfert 2s, the latter assumed to be obscured versions of the former. Here we shall show, as has often been suspected, that the opening angle of the cone depends on the luminosity of the central source, with higher luminosities corresponding to larger opening angles. This conclusion depends only on the assumption that the width of the broad emission lines at a given luminosity is a measure of inclination angle, an assumption that is supported by observation in radio-loud systems. On the other hand we show that the scatter in X-ray spectral index is not primarily an effect of viewing angle, in contrast to what might be expected if the scatter on the spectral index versus luminosity relation were a consequence of absorption in the obscuring material. The observed correlation between linewidth and spectral index appears to be a further consequence of the dependence of opening angle on luminosity.