  The solid-angle sum $A_{\mathcal{P}} (t)$ of a rational polytope
${\mathcal{P}} \subset \mathbb{R}^d$, with $t \in \mathbb{Z}$ was first
investigated by I.G. Macdonald. Using our Fourier-analytic methods, we are able
to establish an explicit formula for $A_{\mathcal{P}} (t)$, for any real
dilation $t$ and any rational polygon ${\mathcal{P}} \subset \mathbb{R}^2$. Our
formulation sheds additional light on previous results, for lattice-point
enumerating functions of triangles, which are usually confined to the case of
integer dilations. Our approach differs from that of Hardy and Littlewood in
1992, but offers an alternate point of view for enumerating weighted lattice
points in real dilations of real triangles.
