Let's consider two triangles ABC and DEF.
All the six angles of both the triangles are known.
And, BC = DE. Now, I form a quadrilateral by combining these triangles such that the side BC or DE is now one of the diagonals of the quadrilateral.
So, what's the angle of intersection of the diagonals of this quadrilateral?
I think this question must be solvable because the shape of both the triangles is fixed and thus the shape of the quadrilateral is also fixed so the angle of intersection of the triangles must also remain fixed.
If both of these triangles are right angled triangles, then the quadrilateral formed by these triangles taking their hypotenuses as diagonal is a cyclic quadrilateral and the angle of intersection can easily be calculated. This is how I got this question, what if the triangles aren't right angled then how I will calculate the angle of intersection.