The complete predicate in this sentence is A. mopped his brow, exhaled sharply, and picked up his phone.
B and C aren't correct, because they aren't complete predicates - something is missing.
D isn't correct, because <em>looking up from his computer monitor </em>is not a predicate, it is an adverb phrase.
B.) serious and impersonal
Adjectives and Adverb phrases relate to prepositional phrases because if you remember what an adjective is, it describes a noun and then an adverb i believe can describe a verb, adjective, and other adverbs. Both adjective and adverb phrases contain prepositions, there fore relating them to prepositional phrases.... I hope this is what you were looking for and answered your question... :)