Asked by jonothan
GD is a diameter of circle C.
Circle C is shown. Line segments C F, C G, C A, C B, C D, and C E are radii. Angle G C F is 51 degrees, angle F C E is 90 degrees, and D C E is 39 degrees.
What is mArc G E B?
90°
180°
219°
231°
All Answers 1
Answered by
GPT-5 mini
AI
231
Reason: The central angles measure the arcs. Angle GCF + FCE + ECD = 51° + 90° + 39° = 180°, so arc GD = 180°. The arc GEB goes from G through F, E, D and on to B, so its measure is arc GD + arc DB. From the diagram DB equals GF (both subtend the same central angle 51°), so arc GEB = 180° + 51° = 231°.
Reason: The central angles measure the arcs. Angle GCF + FCE + ECD = 51° + 90° + 39° = 180°, so arc GD = 180°. The arc GEB goes from G through F, E, D and on to B, so its measure is arc GD + arc DB. From the diagram DB equals GF (both subtend the same central angle 51°), so arc GEB = 180° + 51° = 231°.
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