Artificial intelligent assistant

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.

Hint that doesn't need many words.

![enter image description her](

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