  The nuclei of a wide class of active galaxies emit broad emission lines with
widths at half maximum (FWHM) in the range $10^{3}-10^{4}$ km s$^{-1}$. This
spread of widths is not solely a consequence of the range of the luminosities
of these sources since a plot of width versus luminosity shows a large scatter.
We propose that the broad line emission region (BLR) is axially symmetric and
that this scatter in line width arises from an additional dependence on the
angle of the line of sight to the axis of the emission region. Such a relation
is natural in unified models of active nuclei which link a variety of observed
properties to viewing angle. Adopting a simple form for the line width as a
function of luminosity and angle, and convolving this with the observed
luminosity function, allows us to predict a line width distribution consistent
with the available data. Furthermore, we use the relation between the
equivalent width of a line and the luminosity in the continuum (the `Baldwin
Effect') to predict an observed correlation between line width and equivalent
width. The scatter on this correlation is again provided by angular dependence.
The results have applications as diagnostics of models of the broad line
emission region and in cosmology.
