  Let $\mathcal A$ be a star-shaped polygon in the plane, with rational
vertices, containing the origin. The number of primitive lattice points in the
dilate $t\mathcal A$ is asymptotically $\frac6{\pi^2}$ Area$(t\mathcal A)$ as
$t\to \infty$. We show that the error term is both $\Omega_\pm\big(
t\sqrt{\log\log t} \big)$ and $O(t(\log t)^{2/3}(\log\log t)^{4/3})$. Both
bounds extend (to the above class of polygons) known results for the isosceles
right triangle, which appear in the literature as bounds for the error term in
the summatory function for Euler's $\phi(n)$.
