The emission from nanowires can couple to waveguide modes supported by the nanowire geometry, thus governing the far-field angular pattern. To investigate the geometry-induced coupling of the emission to waveguide modes, we acquire Fourier microscopy images of the photoluminescence of nanowires with diameters ranging from 143 to 208 nm. From the investigated diameter range, we conclude that a few nanometers difference in diameter can abruptly change the coupling of the emission to a specific mode. Moreover, we observe a diameter-dependent width of the Gaussian-shaped angular pattern in the far-field emission. This dependence is understood in terms of interference of the guided modes, which emit at the end facets of the nanowire. Our results are important for the design of quantum emitters, solid state lighting, and photovoltaic devices based on nanowires.