In semi-supervised learning, open-set scenarios present a challenge with the inclusion of unknown classes. Traditional methods predominantly use softmax outputs for distinguishing in-distribution (ID) from out-of-distribution (OOD) classes and often resort to arbitrary thresholds, overlooking the data's statistical properties. Our study introduces a new classification approach based on the angular relationships within feature space, alongside an iterative algorithm to probabilistically assess whether data points are ID or OOD, based on their conditional distributions. This methodology is encapsulated in ProSub, our proposed framework for open-set semi-supervised learning, which has demonstrated superior performance on several benchmarks. The accompanying source code will be released upon publication.