Final answer:
The bolded words 'whether we should study Spanish or German' in the sentence act as a noun clause, serving as the subject complement in the sentence and providing details about the dilemma faced by the speaker.
Step-by-step explanation:
The bolded words in the sentence 'Our dilemma was whether we should study Spanish or German.' form a noun clause. A noun clause is a group of words that acts as a noun in the sentence and often starts with words like 'that', 'what', 'whatever', 'who', 'whomever', 'whichever', and 'whether', as in the case of this sentence. It can serve as the subject, the object, or the complement of a sentence, just like a single-word noun can.
In the provided sentence, the noun clause is acting as the subject complement, telling us more about 'Our dilemma'. It is not modifying a noun, which would make it an adjective clause, nor is it expressing a time, place, condition, contrast, concession, reason, purpose, or manner that would align it with an adverb clause.