The only available tabletop electron storage rings are the machines from the MIRRORCLE series. The electrons are accelerated in a microtron and injected into the storage ring. During its circulation, each electron passes through a tiny target many times, emitting a photon beam. Both the spectrum and the angular distribution of the radiation depend on the material, the thickness and the shape of the target. In this paper measured angular distributions of the radiation from several different targets in the magnetic field of the 20 MeV storage ring MIRRORCLE-20SX are presented. The detector comprises a 3 mm × 3 mm × 8.5 µm plastic scintillator (PS) coupled to a photomultiplier by a bundle of optical fibers. The output of the photomultiplier is digitized by an IF converter. This detector is sensitive mostly to soft X-ray radiation, and its PS is moved by a mechanical system in a plane perpendicular to the radiation axis. The measured angular distributions for Mo and Sn targets contain an annulus which is attributed to transition radiation. The angular distributions for Al, carbon nanotube and diamond-like carbon (DLC) targets show some suppression of the radiation along the magnetic field. This is the first evidence of observation of the angular distribution of synchrotron Cherenkov radiation, which represents Cherenkov radiation in a magnetic field. The power radiated from the DLC target is estimated.