Referring to the figure below (click to enlarge), the length of the green lines are $\displaystyle \sqrt{17}, \sqrt{17}, \sqrt{11}$, and $\displaystyle \sqrt{11}$, how could I find 4 equations in 4 unknowns (not sure that this is the exact amount) for the 4 central angles of the 4 triangles?

Thanks in advance!