3. Which of the following best summarizes the RI.3 relationship, or connection, between the
Western Roman Empire and the Byzantine Empire?
?

You didn't give any option to choose, so I'll explain this question based on the subject.

Explanation:

The first thing you have to consider is that even with the division between the Western and Eastern Empire, the Byzantine Empire maintained several of the traditional roman institutions and laws, and most important, they were the continuation of the Roman Empire. Byzantines call themselves "Roman", and this term - Byzantine - was not used at least until the end of this empire in 1453.  So, as you can see, they didn't break with the Western Empire at all, they just made some changes, especially in religion.