Answer: choice C) 62 degrees
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Explanation:
Mark point D as the center of the circle. Segment EG is the diameter, so angle EDG is 180 degrees. By the central angle theorem, arc EFG is also 180 degrees.
The minor arc from E to F (follow the shortest path along the circle) is 56 degrees. From F to G, along the shortest path, we have y degrees.
(minor arc EF)+(minor arc FG) = arc EFG
56+y = 180
56+y-56 = 180-56
y = 180-56
y = 124
Minor arc FG is 124 degrees.
This is equivalent to saying that central angle FDG is 124 degrees.
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The inscribed angle for minor arc FG is the angle FEG, which is half that of the minor arc measure.
inscribed angle = (1/2)*(arc measure)
angle FEG = (1/2)*(minor arc FG)
x = (1/2)*(124)
x = 62
