As far as I can tell here, is not needed.
Angle JHI is an inscribed angle = one-half of arc JI.
Angle GIH is an inscribed angle = one-half of arc GH.
This means that triangle HIK is isosceles. The vertex angle HKI that your are looking for = 180 - 75 = 105 degrees.
A diameter perpendicular to a chord bisects the chord and its subtended arc.
Now find by subtracting this from 180.