Answering A Question With A Question

When someone answers a question with a question, it is a signal of sensitivity, as the person may be stalling for time to think of the answer.

"Are you doing your homework?

"Who, me?"

Here is from the television program, "The Office" where characters Andy and Angela are engaged, but Andy has just learned that Angela has been with character, Dwight.  It is a comical stretch but it still makes the point of avoidance and sensitivity. 

When a question is avoided, the question itself should be considered sensitive to the subject. 
When the question is answered with a question, the subject needs time to think of an answer, indicating sensitivity. 

Andy: Is it true?
Angela: What have you heard?
Andy: That you're sleeping with Dwight.
Angela: That doesn't sound like me.
Andy: Is it true?
Angela: Andy, I'm engaged to you. I mean, we just signed off on our wedding flowers. Would I have said yes to formal chrysanthemums if I didn't want to get married? And, we went through all that stuff with our wedding cake...
Andy: Just answer the question. Are you sleeping with Dwight?
Angela: A little bit

Here is is again, with emphasis added:

Andy: Is it true?

Angela: What have you heard?

The question, "Is it true?" is a "yes or no" question, making it the easiest to lie to.  

The question about being true, that is, being with the character, Dwight, sensitive.  Always note that when someone answers your question with a question, you've asked an important question and will want an answer. 

Andy: That you're sleeping with Dwight.

Angela: That doesn't sound like me.

This is comical writing!  Note in the language the word "that" showing distance, and the continued avoidance of having to answer the question. 

Andy: Is it true?

Angela: Andy, I'm engaged to you. I mean, we just signed off on our wedding flowers. Would I have said yes to formal chrysanthemums if I didn't want to get married? And, we went through all that stuff with our wedding cake...

The avoidance continues and the subject asks another question.  Is the subject actually speaking to herself?  Is she asking herself why she has done these things?

Andy: Just answer the question. Are you sleeping with Dwight?
Angela: A little bit.

Still avoiding the tension of "yes or no" with minimization.  Comical, but a good example of how humans hate guilt and hate to lie outright.