embroilment vs imbroglio

embroilment and imbroglio both are nouns.

Word	Noun	Adjective	Verb	Adverb
embroilment	Yes	No	No	No
imbroglio	Yes	No	No	No

As nouns, embroilment and imbroglio are synonyms defined as:

embroilment and imbroglio: an intricate and confusing interpersonal or political situation

embroilment (noun)	imbroglio (noun)
an intricate and confusing interpersonal or political situation	a very embarrassing misunderstanding
	an intricate and confusing interpersonal or political situation