Is this inappropriate?

So last night I was mad at my boyfriend, I asked him to leave me alone and give me some space. He volunteered to sleep on the couch which I thought was weird but I like having the bed to myself so whatever. I went to bed, woke up at 4 to the baby crying so I went to get her and noticed he was gone. I texted him and he said he was at the gym with the new girl at work Tracie. I have never known him to go to the gym. The gym is closer to his work so obviously he was planning on going to work after but he doesn’t work till 8:30. So 4 1/2 hours? And that’s only from the time I noticed he was gone. I texted back and said “wow” and he reply’s “it’s not inappropriate at all” and I’m like.. yea it is! He said she’s in her 50s and in a relationship so he wouldn’t even be interested.

The last couple months have been bad. But I didn’t think he would ever cheat on me. Idk what to think

And the last couple months have been bad because I found texts on his phone to another female coworker saying “even married men find you attractive” he said it was an inside joke. Ugh. My trust is broken