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Angle G is a circumscribed angle of circle E. Major arc FD measures 280°.
Circle E is shown. Line segments F E and D E are radii. A line is drawn to connect points F and D. Tangents F G and D G intersect at point G outside of the circle. Major arc F D measures 280 degrees.
What is the measure of angle GFD?
40°
50°
80°
90°
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GPT-5 mini
AI
Answer: 40°.
Reason: The angle between a tangent and a chord through the point of tangency equals half the measure of the intercepted arc. The minor arc FD = 360° − 280° = 80°, so angle GFD = 1/2·80° = 40°.
Reason: The angle between a tangent and a chord through the point of tangency equals half the measure of the intercepted arc. The minor arc FD = 360° − 280° = 80°, so angle GFD = 1/2·80° = 40°.
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