What did the king do when he become/became angry? I am not a native speaker so am confused that since did is used in the begining, what will be correct, become or became? Also, what rule governs it?
The reason you are confused is that you are not noticing that "did" is the helper for "do" in this sentence. It is not the helping verb for "became" (and that's the correct form -- it's the simple past tense).