Circle (2)

2a)

44 + e + 78 = 180
e = 180 - 44 - 78 = 58

To calculate the rest of the angles, we need to add some lines to the diagram as follow:

OGA = 90 (property of tangent)

Therefore OGF = 90 - 44 = 46
OFG = OGF (isosceles triangle)

Similarly OEG = OGE = 12

Finally, we solve the rest as follow

Let OEF = OFE (isosceles triangle) = x

x + x + 12 + 12 + 46 + 46 = 180 (property of triangle)

x = 32

c = x + 12 = 44
d = x + 46 = 78

2b)

The method of solving is similar to 2a)

angle a = 51 (property of isosceles angle)
angle b = 180 - 51 - 51 = 78 (property of triangle) [The answer on the sheet is wrong]
angle d = 51 (similar reasoning as above, skipped here)
angle c = 180 - 51 - 51 = 78 (property of line) [The answer on the sheet is wrong]