In addition to the lengths of the sides, you must have enough information to completely define the polygon. Consider creating a scale model of your room by threading string through straws cut to length. You can imagine that the six-sided figure can assume a variety of shapes.

I suggest measuring the distances between non-adjacent, non-opposite corners. If you identify the corners in sequence with letters A through F, measure between corners A-C, C-E, and E-A, for example. Then you can use a calculator such as this one to find angles.

I suggest measuring the distances between non-adjacent, non-opposite corners. If you identify the corners in sequence with letters A through F, measure between corners A-C, C-E, and E-A, for example. Then you can use a calculator such as this one to find angles.