Your going to have to give more information of the fish environment for anyone to try and figure what's happening. Tank size, water reading, equipment you have, lighting, water changes, heating, etc.... for a starter..
I have a 120 gallon with 1 Vlamingi tang, 2 clowns,1 hawk, 4 green chromis, 1 chocolate chip star and the one Coral beauty. I'm running on a fluval fx5, jbj uv sterilizer and a typhoon protein skimmer with 2 1600 ph powerheads.
I have check them in a week but they were low and I just did a water change on Wed. I do water changes every 2 weeks. The fish acclimated for a hour before I put him in but I noticed he wasn't eating.
How did yoiu acclimate your fish? Float him in the bag or drip acclimate him? You noticed he wasn't eating, in the bag? or in QT? What are you feeding him now?
What seems to be the trouble with current Angel?
Big number that we need is Nitrates and PH. If your water is a big difference from your LFS, then drip acclimation is recommended.
What type of food? Mysis? Squid? Its normal for a fish not to eat for a couple of days after being put into your system, they need to feel safe first. Some will eat right off the bat, if you are feeding the same thing to them that the LFS was feeding him.
Treating the tank for what? And If your treating your tank, you need to get the carbon out of the filter your running. That skimmer is woefully undersized for that tank also.
IMO, best would be to move the fish to a 10g isolation tank and deal with it there. All fish should be introduced to an isolation tank prior to introduction to the display tank. I learned this the hard way. Use the current water in the display tank to fill the isolation tank so the angel will not stress out with the transition. Tangs, clowns, chromis are punks. They could be stressing out the angel as well since it's the latest intro. How long has your tank been running?