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Synonyms for Degree (same or very similar meaning)

WordNet sense 1 (a specific identifiable position in a continuum or series or especially in a process):
level, point, stage

WordNet sense 2 (a measure for arcs and angles):
arcdegree

WordNet sense 3 (an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study):
academic degree

WordNet sense 4 (a position on a scale of intensity or amount or quality):
grade


From the ODE community, based on WordNetadd/edit