Solving Quadrilaterals with Known Angles & 1 Side

[Physics is Phun]

to solve a quadrilateral when you know all four angles and one side? I can't seem to find any way to solve the other 3 sides in this one question I am working on.
thanks

 

[mathwonk]

seems that it should be determined by that data, i.e. the shape should be determiend and then you have one side to set the scale, provided you know which two angles the given side is between. but a formula has not come to mind yet for their lengths.


Wait! what about a rectangle!?

 

[Dburghoff]

No, it's not possible. For example, suppose that all of the angles were right angles. You have one side's length, but how would you know whether the figure is a square or a rectangle? You can't. Suppose the side you are given has length 1, and all the angles are right. The side across from the given side must be 1, but the other two could be anything.

 

[matt grime]

Wait! what about a rectangle!?

Or any other quadrilateral for that matter:

assume that the fixed side is length one and as drawn in the plane is the interval [0,1] on the x axis. extend the sides incident to the ends of this segment to infinity, and draw any line parallel to the side "opposite" our fixed side, then all angles are the same and the other sides can be an uncountable number of options.

 

[mathwonk]

yeah that mental picture conviced me but i thought i would just mention the easy one.