I translated this sentence as "Kateřina is interested in the theater" that was okay, so i guess a theater could also be a correct translation. Sometimes they require specific english words and in my opinion not all possible correct answers are fiatted by the authors it seems.
LongFellow, be careful here. In this particular translation, using 'the' is acceptable because English uses 'the' when talking about theater in general. The Czech sentence does not mean that someone is interested in 'the theater' in the sense of a particular building. Although that would also be 'the theater' in English, the corresponding Czech would then use a demonstrative adjective such as 'to'.
Similarly, if you are talking about a building rather than the art form 'theater', then the Czech sentence here would mean 'a theater'; it would not mean 'the theater' since there is no demonstrative in the Czech.
I find that this DL course is quite consistent in how it permits using 'a' and 'the' in English translations: No demonstrative adjective in the Czech means no 'the' in the English.
The way I learned it growing up in America is that "theatre" is the artform, and "a/the theater" is the building
Interesting discussion! For US English at least, I think both "theater" and "the theater" are acceptable for the general art form, although I think "theater" is more common. But in contrast, for the general art form I would say "interested in music," never "interested in the music" (which to me would always be some specific piece of music).
I've realized that I don't have any consistent rule about when "the" is acceptable for the general form, other than that it's usually not acceptable. Words like "sculpture," "mathematics," "sports" would never carry "the," but a few things to my ear would work either way, like "theater." And some terms, like "the arts" or "the sciences," sound more correct with "the," although you could make it singular and drop the article, i.e. either "interested in the arts" or "interested in art."
"In" zde nechápu, ale kdo by chápal předložky? Může se do věty dát i "about" či "of"?
Ne. To be interested in sb/sth je ustálená slovní vazba.
Vaše otázky se týkají povětšinou angličtiny, doporučil bych vám spíše sousední kurz angličtiny pro česky mluvící.