- She appeared mighty pleased.
- He appears (to be) angry today.
- They do not appear to be happy.
- There appears to be some misunderstanding between them.
- The thieves appear to have left the city.
When appear is used as a copular verb, it is followed by an adjective, not an adverb.
- She appears to be angry. (NOT angrily)
Appear can also be used as a non-copular verb. It then means come into sight, or arrive. In this case it is used with an adverb, not an adjective.
- She suddenly appeared in the doorway.