How do I find the angles of a polygon if I only have the lengths of the sides?

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I have the length of n sides $[l_1,l_2,...,l_n]$ and it is possible to form a polygon using these sides. The sides of the polygon will be in the order as given so the adjacent sides of $l_1$ are $l_n$ and $l_2$ and like that. How do I find the interior angles of the polygon? I know there can be multiple lists of angles for 1 list of sides, I just need any one.

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Two suggestions:

(1) Use the "2-kinks" theorem to form a triangle from your lengths. (Computational Geometry in C, p.330). Then several angles are $180^\circ$, and three are triangle angles.

(2) Form a cyclic polygon from your lengths by shrinking the radius of a circle until your lengths close to a polygon:


          CycPoly
See this MSE posting for cyclic polygon calculations, or the reference by @hardmath (in a comment) to another MSE posting on cyclic polygons.