Question

Please answer the attached question

Answer 1

∠ DFG = 48°

Explanation:

the central angle is equal to the measure of the arc that subtends it.

since EOG is the diameter of the circle with central angle of 180° , then

arc EG = 180°

the inscribed angle EGD is half the measure of the arc ED that subtends it, so

arc ED = 2 × ∠ EGD = 2 × 42° = 84° , then

ED + DG = EG , that is

84° + DG = 180° ( subtract 84° from both sides )

DG = 96°

Then

∠ DFG =
`(1)/(2)` × EG =
`(1)/(2)` × 96° = 48°