  Collinear (small-angle) and large-angle, as well as soft and hard radiations
are investigated in three-jet and Z + two-jet events collected in proton-proton
collisions at the LHC. The normalized production cross sections are measured as
a function of the ratio of transverse momenta of two jets and their angular
separation. The measurements in the three-jet and Z + two-jet events are based
on data collected at a center-of-mass energy of 8 TeV, corresponding to an
integrated luminosity of 19.8 fb$^{-1}$. The Z + two-jet events are
reconstructed in the dimuon decay channel of the Z boson. The three-jet
measurement is extended to include $\sqrt{s} =$ 13 TeV data corresponding to an
integrated luminosity of 2.3 fb$^{-1}$. The results are compared to predictions
from event generators that include parton showers, multiple parton
interactions, and hadronization. The collinear and soft regions are in general
well described by parton showers, whereas the regions of large angular
separation are often best described by calculations using higher-order matrix
elements.
