Angles in a nonagon
The following figure was draw by taking midpoints on three sides of a regular nonagon. The angles are 20 degrees, 50 degrees, and 50 degrees.
![enter image description here](
It's not hard to find the angles by using trigonometry. But, I wonder if it's possible to find the angles without trigonometry.
If you succeed in finding at least one angle without trigonometry, please let me know the way.