Answer:
As the property of angle in a circle:
angle BAC = arc BC = 116 deg
=> angle BHC = (1/2) angle BAC =(1/2) x 116 = 58 deg
angle HCG = (1/2) arc HF = (1/2) x 24 = 12 deg
B, H , G are on the same line, then:
angle BHC + angle CHG = 180 deg
=> angle CHG = 180 - angle BHC = 180 - 58 = 122 deg
Consider sum of three angles in triangle CHG, then:
angle CHG + angle HCG +angle HGC = 180 deg
=> angle HGC = 180 - angle CHG - angle HCG = 180 - 122 - 12 = 46 deg
=> angle BGC = angle HGC = 46 deg
Hope this helps!
:)
