Angrily, in both situations. Sorta. I'll get to that in a moment. "Angry" is an adjective. It modifies nouns. "Angrily" is an adverb. It modifies verbs. If they specify the object, it's absolutely definitely an adverb, because there's no way for that word to modify "the mother". How is she looking at the child? She's looking at the child angrily. Now, if you remove the "at her naughty child" and still want it to mean the same thing, then it's still angrily. How is she looking? She's looking angrily. HOWEVER, if you use an alternative definition of "to look", then A becomes an acceptable choice. Now "to look" means "to appear" instead of "to give a glance". How does the mother look? She looks angry. The mother is angry-looking. Without "at her naughty child", the sentence can mean two different things. Of course, "at her naughty child" is indeed there, and therefore the answer must be B.