Label angle GMJ as $a$ and the other two central angles $b$ and $c$. Call each side of the triangle $s$. You know $a+b+c=360$. Apply the law of cosines to each of the three sub-triangles to get three equations for $s$ in terms of the given lengths and angles $a,~b,~c$. You then have four equations in four unknowns $s,~a,~b,~c$. Have fun.