Explanation:
this an extreme case of 2 lines emanating from the same point crossing through a circle. but the same principles apply.
the angle at J is 1/2 of the difference of the outer and the inner arc angles of the intersected arcs.
the inner arc angle of the HK arc is exactly the angle at G = 138°.
that means the outer arc angle of the arc HK is the remainder of the whole circle arc angle (360°) to the inner arc angle HK
360 - 138 = 222°
so,
angle J = 1/2 × (222 - 138) = 84/2 = 42°