The structure factor and oxygen-oxygen pair distribution functions of amorphous ices at liquid nitrogen temperature (T = 77 K) have been derived from wide-angle X-ray scattering (WAXS) up to interatomic distances of r = 23 angstrom, where local structure differences between the amorphous ices can be seen for the entire range. The distances to the first coordination shell for low-, high-, and very-high-density amorphous ice (LDA, HDA, VHDA) were determined to be 2.75, 2.78, and 2.80 angstrom, respectively, with high accuracy due to measurements up to a large momentum transfer of 23 angstrom(-1). Similarities in pair-distribution functions between LDA and supercooled water at 254.1 K, HDA and liquid water at 365.9 K, and VHDA and high-pressure liquid water were found up to around 8 angstrom, but beyond that at longer distances, the similarities were lost. In addition, the structure of the high-density amorphous ices was compared to high-pressure crystalline ices IV, IX, and XII, and conclusions were drawn about the local ordering.