The error is in the question, not the answer. 'Feel' is wrong: the verb should be 'fall', in whatever tense is appropriate. The most likely tense would probably be the past simple, so the sentence should read "I fell asleep watching TV". In grammatical terms, "watching TV" is a reduced participle clause - a reduction of the subordinate time clause "while I was watching TV". Here's another example: He hurt his ankle playing football = He hurt his ankle while he was playing football Look this grammatical structure up in your grammar book, learn it and practise it. It's a very common pattern and you're sure to meet it again.

The answer is watching, because the sentence is the present continuous tense. He feel asleep while watching tv