Tedious \(I\)Geometry Level 5
Given , a \(\triangle ABC\) which is \(not-obtuse-angled\) .
Now a square , a regular polygon of sides \(m\) and another regular polygon of sides \(n\) are constructed on sides of given triangle.
\(WLOG\) let angle \(A=\alpha\) ,angle \(B=\beta\) ,angle \(C=\gamma\). Such that \(\alpha \leq \beta <\gamma\)
Now centers of square and the 2 regular ploygons when joined form an \(equilateral \) triangle .
Then find \(m+n+ \alpha - \beta + \gamma\) .
Note : All angles are in degrees .