Abstract: The angle measuring system comprises: a first mirror rigidly attached to muzzle end of a long gun barrel in a plane normal to the bore axis; second and third mirrors mounted on the gun mount near each other at the rear end of the barrel facing outwardly at 45.degree. to the bore axis; and a collimated light source positioned to project a primary light ray onto the second mirror at a 45.degree. angle to be reflected to the first mirror and then reflected back to the third mirror. A set of mirrors is mounted in the path of the ray reflected from the third mirror, to split the primary ray into two separate substantially-parallel component rays having vertical components of transverse motion corresponding respectively to the vertical and horizontal components of angular motion of the gun muzzle and first mirror.