Question

They have broken __ their engagement.

Answer 1

The most appropriate word to fill in the blank is 'up'.

'Break up' is a phrasal verb. The Cambridge Dictionary explains, "If a marriage breaks up or two people in a romantic relationship break up, their marriage or their relationship ends".

Since the purpose of the speaker in this sentence is to inform the reader about the end of the engagement; therefore ‘up’ is the correct option to fill in the blank here.

They have broken up their engagement.  

Given above is the most suitable answer to the question.