How to understand the -하다고 suffix?

Question

I found myself completely unable to explain the -하다고 suffix to someone. For example,

행복하다고 느낍니까?

which means, "Do you feel that you're happy?"

Actually, no, there's a nuance there. I think it translates more like, "Would you say that you feel happy?" Because, let's take it back: it could have just been

행복해요?

which means, "Are you happy?" But we're trying to add emphasis (to something, I don't know what).

What I know is

• 행복 means "happiness."
• 행복하다 means "I am / You are / [Subject is] happy."
• 행복하다고 means ???. (The "고" here is not the conjunctive "고"!)

It's almost as if the "고" here actually "quotes" its preceding phrase as a hypothetical, so that the literal translation of the original is:

Is "I am happy" a thing that you feel?

I'd appreciate a cleaner and more formal understanding of this construction. Thank you.

Answer 1

-(하다)고 corresponds, more or less, to English "that". It packages the whole inner sentence so that it can be used as an object of the outer verb.

행복하다고 느낍니까? = Do you feel that you are happy?

행복하다고 생각한다. = [I] think that I am happy.

행복하다고 말했어요. = [He] said that he was happy.

주민들이 행복하다고 주장했습니다. = They insisted that the residents are happy.

Answer 2

고 means indirect quotation

요즘, 행복하다고 느끼나요 ?

This sentence can be used in the following situation :

A : C earn a big money so that C is happy

B : Oh.

B : I heard that you are happy 요즘 행복하다고 하던데.

C : Sure.