Dorothy was always speaking highly of her role in the play,__,of course, made the others unhappy.

很明显是标准的which指代前一句话的非限制性定语从句，有两种情况可以用this:句子中间是“；”或this前见and.但此处必须用which!

which- indicates her role in the play

you can use thia but you must break this sentence into two.
So, full stop after 'play'...then you can use 'This'

留意标点:Dorothy was always speaking highly of her role in the play.This,of course, made the others unhappy.

this 不能做关系词

我怎么觉得这个就是应该用this呢，没有语法知识，只是觉得，向来都是这样做题的

因为这是一句话，which代替前面的“Dorothy was always speaking highly of her role in the play”。如果中间用句号隔开，就可以用this了

非限制性定语从句表一件事情用which或that,此处用which,