The answer to "Which best identifies the sentence that contains a misplaced modifier?" is C: (Drawn to the best of his ability), the art judges were very impressed by it.
A misplaced modifier is a phase, word or clause that is separated from the word it describes or modifies.
In this case the misplaced modifier( "drawn to the best of his ability") is a misplaced clause which is supposed to describe how the work("it") was made. The best way to fix a misplaced clause is to put it next to the word it is meant to modify (The art judges were very impressed by the work drawn to the best of his ability)
