We are given the angles and side lengths of a polygon $a,b,...$ and $A,B,...$ like so: (the polygon has non-negative side lengths and is convex)
How can we find out whether a polygon with these angles/sides actually exists?
We could start at one vertex and go around the corners of the polygon using trig functions making sure that the final coordinates match the initial coordinates.
e.g. for the quadrilateral above
$c+d \cos(\pi-C) + a \cos(2\pi-C-D) + b \cos(3\pi-C-D-A)=0$ $d \sin(\pi-C)+a \sin(2\pi-C-D)+b\sin(3\pi-C-D-A)=0$
We could square and add these to get a single equation.
Are there any other necessary and sufficient conditions like that? I am especially interested in conditions that don't use trig functions, if there are any. Thanks!