Three masses A$,$ B and C are placed on a balanced disc at radii of $80$ mm$,60$ mm and $100$ mm respectively. The angles between successive masses are $1350$ and $900,$ shown in the figure below. The mass A is $1\mathrm{.}2$ g$,$ and the mass B is $2\mathrm{.}2$ g$.$ The mass C is in the question below. Find the fourth mass position in degree, which should be added at a radius of $50$ mm in order to balance the system. The angle should be within $360$ degrees. Please see details below.