-다가 — and then

This expression is used to indicate the speaker's interruption of one action to immediately start doing mother action. -다가 can be shortened to the form -다.

Details

1. This expression is also used to indicate that the action in the preceding clause continues while the action in the following clause occurs.

잠을 다가 무서운 꿈을 꿨어요.

I was sleeping and had a scary dream.

길을 걸어가다가 갑자기 생각이 나서 전화했어.

I was walking along and suddenly thought (of you), so I called.

친구하고 이야기를 하다가 웃었어요.

I was talking to my friend and laughed. (= laughed while talking to my friend)

2. The subject of the preceding and following clauses must be the same.

(내가) 밥을 먹다가 전화가 왔습니다. ✕

The sentence is ungrammatical because the subject of 전화가 왔습니다 is 전화. So it has a different subject from the preceding clause.

Kimchi Reader

Expresses the speaker's interruption of one action to immediately start another action.

Details

'가' is sometimes omitted with no change to the meaning.