Can a non-convex polyhedral angle have the sum of plane angles smaller than $180^\circ$?
I don't have a fully-fledged attempt. I've only been able to gather some potentially useful facts.
Here's what I got:
Given: non-convex polyhedral angle SABCD, where sides ASD and DSC are concave.
- $|ASD-DSC| < ASC < ASD+DSC$
- |difference of two plane angles adjacent angles| < angle < sum of two adjacent angles
I'm sure the answer is "no", out of intuition. How can I prove it, though?