A logic problem by Andric Kim

There is an angel that answers a question using only "true or false". This angel has the following characteristics:

This angel only tells the truth.

In any case, this angel must answer using only "true or false".

If the angel said "true", then the question is absolutely true, and if the angel said "false", vice versa.

This angel knows everything.

Nevertheless, 1. You cannot ask a question that can not be answered using "true or false" like "what is the color of the sky?". 2. You cannot ask a question that contains the argument that does not make any sense.

When the angel was asked for a one-sentence question, this angel could not answer to it.

Which question did you ask?

1. Are you going to answer "false" to this question?
2. Are you going to answer "true" to this question?
3. Can you answer "false" to this question?
4. Can you answer "true" to this question?

(The phrase "Can you...?" or "Can't you...?" does not refer to a request, but it refers to the possibility, whether this angel can or can't answer according to the question.)

Note: There could be several alternative answers. Not only the one that I put is correct! Try to find yourself another solution. (For example, "Do you know something that you don't know?" is another alternative solution for this problem.)