V/A+ 던가요?

It is attached to the stem of an action verb or a descriptive verb to ask about the past event that the listener has experienced in the past.

It’s a form of asking a question by adding ‘-ㄴ가요?’ to ‘-더’, the regretting expression. Expressions that include ‘더’ such as ‘-더군요’, ‘-던데요’, and ‘-더라고요’ is usually used in the answer, too.

가 : 학생들이 연주는 다 잘하던가요?
Were all the students good at playing?
나 : 아직 학생이라 조금 부족하긴 하더군요. 그래도 좋은 연주였어요.
They were a little short because they are still students. But it was a good performance.

가 : 유양 씨는 건강하던가요?
Was Yooyang healthy?
나 : 네, 생각보다 잘 지내고 있더라고요.
Yes, she was doing better than I thought.

가 : 어제 해수욕장이 개장했더라고요. 그래서 오랜만에 바다에서 수영했어요.
I found the beach opened yesterday. So I swam in the sea for a long time.
나 : 어제 날씨가 꽤 쌀쌀하던데 춥지는 않던가요?
It was quite chilly yesterday, wasn’t it cold?

Conversation:

주말에 부산으로 여행을 다녀왔다면서요? 부산은 어떻던가요?
I heard you went on a trip to Busan last weekend. How was Busan?

저는 다른 것보다 그 지역 사람들이 사용하는 말투가 제일 흥미로웠어요.
More than anything else, I was most interested in the way that people in the area speak.

부산 사투리의 억양은 표준어와 좀 다르지요?
The Busan dialect accent is a little different from that of the standard language, isn’t it?

네, 그리고 성조가 있다는 느낌까지 들었어요.
Yes, and I even felt there is even an intonation.

맞아요. 경상도 사투리는 다른 지역의 말에 비해서 음의 고저가 있는 편이에요.
You’re right. Gyeongsang-do dialect tends to have a pitch that the word of other areas.

단어나 표현이 다른 것도 있어서 처음에는 이해하기가 힘들었는데 듣다 보니 나중에는 이해돼서 신기하더라고요.
At first, it was hard to understand because there were some different words and expressions but I could understand them as I listen to them, and I felt surprised.

Related words
사투리 dialect
억양 accent
표준어 standard language
성조 intonation
(음의) 고저 pitch

Source: Yonsei University. Korean Language Institute