Nowadays, superconducting high field magnets are used in numerous applications due to their superior properties. High temperature superconductors (HTS) are usually used for production of circular pancake or racetrack coils. However different geometries of HTS coils might be required for some specific applications. In this study, the HTS coil wound on a rectangular frame was fully characterized in homogeneous DC background field. The study contains measurements of critical current angular dependencies. The critical current of the entire coil and two selected strands under different magnitudes and orientations of external magnetic fields are measured. The critical regions of the coil in different angular regimes are determined. This study brings better understanding of the in- field performance of HTS coils wound on frames with right-angles.