Slept with my ex, am I a horrible person?

I dated my last girlfriend for 3 years before breaking up with her after a trip we took together. She told me and My family before our flight that she was going to move in with a guy from work. It made me furious and I told her I'd prefer if she wanted to move out that it be with me. Once we broke up she moved in with the guy and they were sleeping together and in a relationship only a week later. Now only 2 months after breaking up they are engaged.
Recently she came over just to hang out and watch a movie and we ended up having sex. First of all was she cheating on me before we broke up?
And Second, does it make me a bad person having slept with her now that she is engaged?
Slept with my ex, am I a horrible person?
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