wage vs engage

wage is a noun but engage is not a noun.

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

As verbs, wage and engage are synonyms defined as:

wage (noun)	engage (noun)
something that remunerates

wage (verb)	engage (verb)
carry on (wars, battles, or campaigns)	get caught
	consume all of one's attention or time
	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)