Electron scattering in the topological surface state (TSS) of the topological insulator Bi1.5Sb0.5Te1.7Se1.3 was studied using quasiparticle interference observed by scanning tunneling microscopy. It was found that not only the 180° backscattering but also a wide range of backscattering angles of 100°-180° are effectively prohibited in the TSS. This conclusion was obtained by comparing the observed scattering vectors with the diameters of the constant-energy contours of the TSS, which were measured for both occupied and unoccupied states using time- and angle-resolved photoemission spectroscopy. The robust protection from backscattering in the TSS is good news for applications, but it poses a challenge to the theoretical understanding of the transport in the TSS.