@brazilianengstudent,
Your professor is absolutely right.
An adjective is a word that modifies another word. 'These' modifies 'lines.' 'Their' modifies 'strengths'. 'All' modifies 'complaints.' "Another' modifies nothing. In this particular sentence, in fact, it serves as an abstract noun.
There's nothing wrong with the way the question was written. What's wrong here is the use of that particular sentence as an example of the use of adjectives. I agree with you that it's somewhat unfair.