So I have 4 collections of lines drawn between points each making a path. The angles are measured. The problem I am attempting to solve is to determine whether or not each of the collections of points are a valid path between some subset of points on a regular 13-gon. So for instance, for the second shape are there 3 vertices in a regular 13 gon such that drawing a line between them gives a 60 degree angle (within 5 degrees of error, see context). I'm having a hard time figuring this out myself. I know the geometry involved but I'm just having a hard time applying it to this problem.
The context of this problem is actually a clue given in the hunt for the secret zoo level of the video game Accounting Plus VR and this was my attempt to solve what these diagrams mean. So because I measured the angles with an actual protractor they have 5 degrees of precision. So if there are valid points with approximate angles that is also a valid answer. I hope this doesn't make the question unanswerable but this is what I have to work with geometry wise. This is effectively an actual "real" problem with imperfect diagrams, rather than an ideal theoretical problem coming out of a book.
And yes the images are the original images I obtained for reference blown up in size. So if one wants to remeasure the angles in case my protractor skill is flawed, they are welcome to.