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Interesting math problem
Because the circle is inscribed with pentagons and all sides are equal, and both sides and the corresponding radius are congruent to form a triangle, as shown in the figure, so ∠ 1=∠2=∠3=∠4, so there is ∠5=∠6.

Similarly, other angles are equal.

This is a regular pentagon.

I hope it can be adopted.