Finding a relationship between angles

[A2024]

Hello,

In the attached image, is there a way to find the alpha angles, if we know the value of the beta angle? All 4 alpha angles are equal, the 3 segments in between are equal, and lines as shown there are always collinear. Please see attached file. Thank you in advance.

 

[Alonzo]

Good problem. I've been working on it a bit for a few days. Nothing to report yet. Given the obvious symmetry (right?) - there should be a solution.