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degree has 6 distinct synonyms spread across 4 of its 7 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
Synonyms, antonyms and the broader and narrower relations for degree come from Princeton University’s WordNet. Full sources and licences.
a specific identifiable position in a continuum or series or especially in a process
“a remarkable degree of frankness”
an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study
“he earned his degree at Princeton summa cum laude”
a measure for arcs and angles
“there are 360 degrees in a circle”
the highest power of a term or variable
a unit of temperature on a specified scale
“the game was played in spite of the 40-degree temperature”
the seriousness of something (e.g., a burn or crime)
“murder in the second degree”