Question

Compliment: 1. (noun) an expression of admiration or praise 2. (verb) to praise somebody complement: 1. (noun) something that completes, makes up a whole 2. (verb) to complete something Read the sentence. The bronze statue was a lovely __________ to her collection. Which word correctly completes the sentence?

Answer 1

Compliment is a noun which is an expression of admiration and praise. 
Complement, on the other hand, is also a noun that completes making up a whole. In the sentence, the word that you should use is COMPLEMENT. 
The bronze statue was a lovely complement to her collection. 

Answer 2

The correct answer is complement.

Like you wrote above, to complete is when you make something whole. Complement is something that completes your collection. The bronze statue completed her collection perfectly, which is why it was a good complement. Somebody can give her a compliment on her complement, however, meaning that he or she can praise the statue. :)