engage vs plight

engage is not a noun while plight is a noun.

Word	Noun	Adjective	Verb	Adverb
engage	No	No	Yes	No
plight	Yes	No	Yes	No

As verbs, engage and plight are synonyms defined as:

Other synonyms of engage include affiance, betroth.

engage (noun)	plight (noun)
	a solemn pledge of fidelity
	a situation from which extrication is difficult especially an unpleasant or trying one

engage (verb)	plight (verb)
get caught	promise solemnly and formally
consume all of one's attention or time	give to in marriage
give to in marriage
keep engaged
engage for service under a term of contract
hire for work or assistance
ask to represent; of legal counsel
engage or hire for work
carry out or participate in an activity; be involved in
carry on (wars, battles, or campaigns)