  We present a study of the Angular Resolution of the AGILE gamma-ray imaging
detector (GRID) that is operational in space since April 2007. The AGILE
instrument is made of an array of 12 planes each equipped with a Tungsten
converter and Silicon micros trip detectors and is sensitive in the energy
range 50 MeV - 10 GeV. Among the space instruments devoted to gamma-ray
astrophysics, AGILE uniquely exploits an analog readout system with dedicated
electronics coupled with Silicon detectors. We show the results of Monte Carlo
simulations carried out to reproduce the gamma-ray detection by the GRID, and
we compare them to in-flight data. We use the Crab (pulsar + Nebula) system for
discussion of real data performance, since its E^{-2} energy spectrum is
representative of the majority of gamma-ray sources. For Crab-like spectrum
sources, the GRID angular resolution (FWHM of ~4deg at 100 MeV; ~0.8deg at 1
GeV; ~0.9deg integrating the full energy band from 100 MeV to tens of GeV) is
stable across a large field of view, being characterized by a flat response up
to 30deg off-axis. A comparison of the angular resolution obtained by the two
operational gamma-ray instruments, AGILE-GRID and Fermi-LAT, is interesting in
view of future gamma-ray missions, that are currently under study. The two
instruments exploit different detector configurations affecting the angular
resolution: the former being optimized in the readout and track reconstruction
especially in the low-energy band, the latter in terms of converter thickness
and power consumption. We show that, despite these differences, the angular
resolution of both instruments is very similar between 100 MeV and a few GeV.
