A method is described for measuring angular distributions of momentum-integrated secondary-particle fluxes from high-energy accelerator targets by studying gamma-ray spectroscopically spallation reactions induced in foils placed around the targets. Results obtained for different threshold energies at 15- to 165-deg angles with copper foils at 22 GeV/c at the CERN Proton Synchrotron are presented. They are further interpreted with the aid of calculated spallation cross sections and compared with good agreement to the results of Monte Carlo computations of hadronic cascades.