Syllable division derived from spelling — this word is not in the pronouncing dictionary, so no phonetic transcription is shown rather than a guessed one.
unengaged is an adjective meaning "not busy or occupied; free". It carries 2 recorded senses.
not busy or occupied; free
“the cancellation left her unengaged a good part of the afternoon”
not promised in marriage
“continued seeing him but on an unengaged basis”
Definitions, synonyms and semantic relations for unengaged come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.