We describe the formation of bulk and edge arcs in the dispersion relation of two-dimensional coupled-resonator arrays that are topologically trivial in the Hermitian limit. Each resonator provides two asymmetrically coupled internal modes, as realized in noncircular open geometries, which enables the system to exhibit non-Hermitian physics. Neighboring resonators are coupled chirally to induce non-Hermitian symmetries. The bulk dispersion displays Fermi arcs connecting spectral singularities known as exceptional points and can be tuned to display purely real and imaginary branches. At an interface between resonators of different shape, one-dimensional edge states form that spectrally align along complex arcs connecting different parts of the bulk bands. We also describe conditions under which the edge-state arcs are freestanding. These features can be controlled via anisotropy in the resonator couplings.