Azimuthal correlations between the two jets with the largest transverse momenta p(T) in inclusive 2-, 3-, and 4-jet events are presented for several regions of the leading jet p(T) up to 4 TeV. For 3- and 4-jet scenarios, measurements of the minimum azimuthal angles between any two of the three or four leading p(T) jets are also presented. The analysis is based on data from proton-proton collisions collected by the CMS Collaboration at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1). Calculations based on leading-order matrix elements supplemented with parton showering and hadronization do not fully describe the data, so next-to-leading-order calculations matched with parton shower and hadronization models are needed to better describe the measured distributions. Furthermore, we show that azimuthal jet correlations are sensitive to details of the parton showering, hadronization, and multiparton interactions. Anext-to-leading-order calculation matched with parton showers in the MC@NLO method, as implemented in HERWIG 7, gives a better overall description of the measurements than the powheg method.