Enter the word that best completes the sentence.
word bank
straits sheer obstinate
rumor agonize luxurious
i knew my cousin would
over the news all night, so i saved her the worry and didn’t tell her.

I knew my cousin would agonize over the news all night, so I saved her the worry and didn't tell her. 
The reason your answer is agonize is because, to agonize is to be distraught while thinking of something, so by saving her the worry her cousin had no reason to agonize the news or situation. 
I hope this helps! 

This is a compound sentence because it uses fanboys the s stands for since.