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The theorem that is used extensively here is that the angle subtended by an arc of a circle at the centre is double that subtended at the circumference within the other arc.
I cannot read the label of the point where EG meets the circle again and I am going to call it I.
Then
IVN = 74 => IGN = 37
NVA = 112 => NGA = 56
AVT = 32 => AGT = 16
Then
IGT = IGN + NGA + AGT = 109
=> EGT = 180 - IGT = 71 (angles on a straight line).
Now IVG (Reflex) = IVN + NVA + AVT + TVG = 74 +112 + 32 + 18 = 236
so IVG (Minor) = 360 - 236 = 124 => ITG = 62
IVN = 74 => ITN = 37
Then GTN = GTI + ITN = ITG + ITN = 62 + 37 = 99
=> ETG = 180 - GTN = 81 (angles on a straight line).
Finally, in triangle GET, GET = 180 - (EGT + ETG) = 180 -(71 + 81) = 28
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