  An analysis of angle-resolved photoemission (ARPES) experiments in the
superconducting state of the high \tc copper-oxides is presented. It is based
on a phenomenological weak-coupling BCS model which incorporates the
experimental normal state dispersion extracted from ARPES, and non-magnetic
impurity scattering in the presence of a $d_{x^2-y^2}$ order parameter (OP). It
is shown, that already in the pure case, the broadening by finite momentum
resolution of the analyzer leads to a finite region of apparent `gaplessness'
around the true node of the OP. Non-magnetic impurities further amplify this
effect by introducing additional spectral weight around zero frequency. At
sufficiently large impurity concentrations $n_i\approx 0.02-0.05$, this results
in an extended region of `gaplessness' up to $\delta\phi=\pm7$ ($\phi$ the
angle on the Fermi surface) around the true node for a large range of moderate
to strong impurity potential strengths. Different ways to identify the presence
of impurity scattering in the ARPES spectra are proposed.
