Answer:
Second Sentence: My family was delighted by the puzzling mystery of the film.
Step-by-step explanation:
Present participle is word formed by adding -ing at the end of a verb.
Adjective: is word which modifies, describes or gives an attribute to a noun, e.g in "black color", "black" is an adjective. In "I had a nice time there" , nice is an adjective. There are many methods of forming adjectives and similarly many types of adjectives. For the purpose of brevity, let's just talk about present participle adjective.
Present Participle Adjective: The adjective formed by adding -ing after the present indefinite form (first form) of the verb is called present participle adjective, in contrast to past participle adjective which is formed by adding -ed after the first form of the verb. For example, in "he had a frightening experience", "frightening" is present participle adjective modifying "experience"
In the sentence selected, "puzzling" is present participle of puzzle, which is modifying mystery (a noun). Hence it is a present participle adjective.
"living" in first sentence, "wondering" in third sentence, and "playing" in fourth sentence are functioning as principal verbs in the sentences.