Solid angle of a polyhedral cone, which indicates the proportion of space occupied by the cone, is of significant interest in discrete optimization. Gomory introduced the cyclic group relaxation of IP. The facets of the cyclic group polyhedra are useful in generating cutting planes. To predict the importance or relative size of each facet, researchers have used the shooting experiment, which provides an estimate of the solid angle subtended by the facet at the origin. However, the obtained sizes were not always consistent due to randomness. We propose to use the solid angles measure, whose closed formulas were well established in two and three dimensions. For higher dimensions, Aomoto and Ribando showed that the solid angle of a simplicial cone can be computed using a multivariable hypergeometric series, provided that the cone satisfies a certain condition related to positive-definiteness. We provide decomposition methods to ensure that the positive-definite criterion is met. We present our results of the solid angle measures and compare them with those obtained from the shooting experiments.