Calculate coordinates of polygon's points after changing lenght of one side

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I have a list of points (vectors) on the surface, together they form a polygon. Two sides lead from each point, each side has only two points, these sides form the polygon.

And my problem is: How to calculate the new coordinates of all points, if I wanted to enlarge or shorten one side of the polygon to a given length so that all other side lengths remained the same, only the inner angles of the polygon and the selected side would change.

Thanks for your help.

EDIT: Moved line should be parallel to past self, because previous version of this question had infinite number of solutions, so this version should have only zero or one solution.

Again thanks for your help.