Answer: 110
Explanation
The four central angles add up to 360 degrees, since they sweep out a full circle.
I'll start at the top and move clockwise to add up the angles shown.
(8x+22)+(8x-27)+(17x-57)+59 = 360
33x - 3 = 360
33x = 360+3
33x = 363
x = 363/33
x = 11
Then,
angle HGK = 8x+22 = 8*11+22 = 110
