애정관계(not 게) means "relationship (normally) between couples." 관심(interest) ------> 호감(good feeling) ------> 사랑(love) 1) -에 관심이 있다 or 관심을 갖다 means "to be interested in sth" or "have an interest in sth" for example, 나는 한국어와 한국 문화에 관심이 있다. I'm interested in Korean language and culture. 2) -에게/한테 호감이 있다 or 호감이다 means "have a good feeling" or is used to refer to "a person who make a favorable impression". Actually it can be translated in various ways like "to start to show interest in someone, to be prepossessed by, to find oneself increasingly attracted to someone, etc." for example, 나는 그 남자에게 호감이 있다. 나는 그 남자의 매너에 호감을 느낀다. I am prepossessed by his manners.

(애정관게 incorrect)애정관계 means you are now in a state of love with each other. Simply, bf and gf. It can be different meaning what kind of adjectives are on the front side. e.g. 불안정한 애정관계 [unstable relationship], 긴밀한 애정관계 [close love affair] etc. 관심 has different meaning situation by situation, it can be simply interests which you really like to know about inforamtions. Similar to curiousity. For example, starting new exercising, reading books, etc. Or it is interest about who you really like. Such as intriguing your interests like pop stars, celebrities. 호감 is different with 관심 you already interested in something or somebody and you really like that. The antonym of 호감 is 반감. So basically 호감 is you have like, 반감 is dislike. For easy understanding, 호감 is you are likely to close to something or somebody, stay with good state and get positive feedback to you. It could be peoples, things, religions, anything.

Hi Alina. Firstly, *애정관계 is correct word :) In terms of your question, both have basically same meaning. If it's translated to english, INTEREST could be acceptable. e.g 나 그 남자한테 관심있어/호감있어 means, "I think I like it or I'm interested in him." (Personally not sure you say like that in English tho, hopefully you got the basic idea) One of the differece between two words would be the kind of "Objective" You can say "나 그 남자한테 관심있어." and also "나 그 새로나온 영화에 관심있어." However, "호감" can't be used with "things". As using same contents above, you are able to say "나 그 남자한테 호감있어", but unable to say "나 그 새로나온 영화에 호감있어", it sounds weird and we don't say it. Wish my answer could help you. Night night:) oh, nearly forgot answering the first question. 애정관계 means "The relationship in a couple". But tbh, it isn't really used in normal life, i reckon. If you have a full sentence, just let me know. :)