A theory of the open-orbit magnetoresistance of potassium, discovered by Coulter and Datars, is developed. The open orbits caused by the multiple periodicities of a charge-density-wave (CDW) state are derived. Since a single crystal consists of domains, each having its CDW wave vector along one of 24 preferred axes, we employ effective-medium theory to calculate the magnetoresistance rotation pattern. The effects of domain texture and size are illustrated. The magnetic field at which open-orbit peaks appear depends on the domain size, which we find to be ~0.1 mm. The rotation pattern at 24 T is calculated in order to exhibit the detailed information that becomes available at extremely high fields. High-field experiments would aid in the determination of open-orbit directions and allow magnetic-breakdown studies of the energy gaps.