Given a diagram of n infinitely long straight lines in the plane, let them intersect in the points p_i, let the angles at $p_i$ be $v_i^j$, such that $360=\sum_j v_i^j$.
Given the suggestive diagram, and some angles, if one is given the task of calculating some $v_m^n$, and the diagram and angles determine this angle uniquely, is it always sufficient for finding this angle to solve the linear system $360=\sum_j v_i^j$ for every i, together with $a+b+c=180$ for every triangle?
One cant read any distances or other things off the diagram, only the order in which line a intersects line b, for every a, for every b.
What if one is given some additional information, that some distances are equal? Is it necessary to draw any more straight lines? Does one never need any more advanced formula/geomtry to find $v_n^m$?
(Why) does the algorithm fail for http://www.cut-the-knot.org/triangle/80-80-20/60-70Sol1.shtml#solution