I would begin with as huge as possible water change, keep temperature steady, if possible around 74F -most harmful bacteria would slow down its growth rate at this temp-, and improve availability of dissolved oxygen -by lowering the water line an inch so the output of the filter hits the water harder- however you need to have some calm areas in your tank for the Angelfish comfort.
Something is going on in your tank and you probably won't be able to know what it is: so focus on solutions.
Please post the following info:
Tank volume and dimensions, age of tank, filtration system, substrate, tankmates (list actual as well as recently), as well as actual readings of ammonia, nitrite, nitrates, pH, and Temp.
Hope you can save the survivors. I agree with the hypothesis that some virulent bacteria entered your tank with the newly added fish; however, other possibilities include cycle disruption, low levels of dissolved oxygen and pH instability.
Pepe
Santo Domingo