어/아/여 다가 = and then
After an action is done in the first part of the sentence, a following action takes place based on the first actions results. eg. I took a book, “and then” gave it to my friend.
Example of 어/아/여 다가
은행에서 돈을 찾아다가 영화를 봤어요. I withdrew money from the bank, and then watched a movie.
밥을 먹다가 졸았어요. I was eating, and then dozed off
자정거를 타다가 넘어져서 다쳤어요. I was riding the bike, and then fell and hurt my self.