To complete @SANGYOON CHOI answer.
Most of time you can use `~하게 하다` to mean `make (sb) feel ...`
~하게 하다 is (verb) + 게 + 하다.
게 has similar sense with `in this state`. It is used to construct adverbs. For instance for the verb 슬프다 (sad) It would become 슬프게 (sadly, in a sad state, in a sad manner).
하다 is `to do`, `to make`. Therefore ~게 하다 is `to make (sb/sth) in a certain state/way`.
Keep in mind there is also a direct way to express what you've asked for. For instance,
그가 때문에 저는 화가 나요. (I feel angry because of him).