The precise momentum dependence of the superconducting gap in the iron-arsenide superconductor Ba1−xKxFe2As2 (BKFA) with Tc=32 K was determined from angle-resolved photoemission spectroscopy (ARPES) via fitting the distribution of the quasiparticle density to a model. The model incorporates finite lifetime and experimental resolution effects, as well as accounts for peculiarities of BKFA electronic structure. We have found that the value of the superconducting gap is practically the same for the inner Γ barrel, X pocket, and “blade” pocket, and equals 9 meV, while the gap on the outer Γ barrel is estimated to be less than 4 meV, resulting in 2Δ/kBTc=6.8 for the large gap and 2Δ/kBTc<3 for the small gap. A large (77±3 %) nonsuperconducting component in the photoemission signal is observed below Tc. Details of gap extraction from ARPES data are discussed in Appendixes A,B.