After some minor debates with others, the NGINX Stable and Mainline PPAs have been updated to include builds for the armhf architecture. This means that individuals running Ubuntu Precise 12.04, Trusty 14.04, Utopic 14.10, or Vivid 15.04 (although I have no idea why you’d be using this version in production) on armv7 architecture (which is armhf architecture) will be able to add the PPA and install the NGINX packages as if they were on a standard 64bit or 32bit server.
Shoutout to William Grant for helping to get the two staging PPAs I use for building the packages set up with ARM builds. Didn’t take much to do, but each little bit of assistance to move the PPAs forward towards the modern era helps, so thanks, William Grant for your assistance in turning on ARM builds for the PPAs.