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Answer: Choice B) Angle EGH
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The given angle is DGE. Exactly two of the letters (D, G, and E) will be found in any adjacent angle to this given one. For example, angle FGD is adjacent to DGE because of the shared letters D and G. The two angles share the segment DG.
Similarly, angle DGE is adjacent to EGH for the same reason. Now segment EG is the overlapping shared segment. Note how "E" and "G" can be found in the given angle and the answer.
Edit: see the attached image for visual proof. The given angle is in red. The angle for the answer is in blue.
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The given angle is DGE. Exactly two of the letters (D, G, and E) will be found in any adjacent angle to this given one. For example, angle FGD is adjacent to DGE because of the shared letters D and G. The two angles share the segment DG.
Similarly, angle DGE is adjacent to EGH for the same reason. Now segment EG is the overlapping shared segment. Note how "E" and "G" can be found in the given angle and the answer.
Edit: see the attached image for visual proof. The given angle is in red. The angle for the answer is in blue.