Given the two angles $\alpha_1$ and $\alpha_2$ in which a vertex angle of a triangle is split by the related median $m$, find the remaining angles of the triangle $\beta$ and $\gamma$.
I encountered this problem in my research, I think that it is well defined and definitely solvable, but I cannot find the right approach.
By applying the sine law for triangles $ABM$ and $AMC$, you can get that $\frac{sin \alpha1}{sin \alpha2} = \frac{sin \beta}{sin \gamma}$ holds true. Since problem statement indicates the given angles $\alpha1$ and $\alpha2$, using triangle's angles summation property, one would find $\gamma = 180 - \alpha1 - \alpha2 - \beta$ with known ratio $\frac{sin \beta}{sin (\alpha1 + \alpha2 + \beta)}$. I guess it would be obvious afterwards to evaluate the desired angle $\beta$.