We've been using Hall effect sensors for lid close detection for a long, long time. My thinkpad from 2013 has it halfway down one edge.

If you simply move the sensor (that is already a requirement) closer to the hinge, you can infer angle based on the Hall sensor for free. You can even get special sensors that specifically measure the magnetic field orientation for the same price as the simple type.

Yes, it's completely free with just a very minimal amount of thought put into the design.