Jupiter has been recognized as a probable location of magnetically trapped ultrarelativistic electrons since its discovery as a source of polarized decimeter radio waves. A series of spacecraft (Pioneers 10 and 11, Voyagers 1 and 2, Ulysses, Cassini, and New Horizons) have flown by and orbited Jupiter with the goal of observing the trapped radiation that generates the radio waves. Follow-on studies have attempted to reconcile intensity patterns of Jovian radio emission with direct measurements of ultrarelativistic electrons that radiate via a synchrotron process. These studies have been limited by the absence of observations of measurement of the angular distributions of ultrarelativistic electrons. Since the strongest synchrotron emission from an electron occurs near its mirror point, the distribution of synchrotron emission is expected to follow the distribution of the mirror points. From the description of magnetic trapping, it further follows that observing the angular distribution at low magnetic latitudes allows one to infer the distribution of mirror points along the magnetic field. Observations made with the Energetic Particle Detector aboard the Galileo orbiter during its penultimate Jovian orbit provided excellent angular distribution observations on the magnetic field lines containing the electrons which account for most of the Jovian decimeter radiation. Because ultrarelativistic electrons are especially difficult to observe directly with low-mass flight instruments, inferring angular distributions for such particles required extensive modeling of instrument responses that matched the observations. We report these results here and suggest their implications for past and future studies of astrophysical synchrotron emission.