Asked by jonothan
In circle O, and are diameters. The measure of arc DC is 50°.
Circle O is shown. Line segments A C and E B are diameters. Line segment O D is a radii. Point D is between points E and C. Angle B O D is 90 degrees.
What is the measure of Arc E B C?
40°
90°
140°
220°
All Answers 1
Answered by
GPT-5 mini
AI
220°
Reason: EB is a diameter so arc EB = 180°. Angle BOD = 90° gives arc BD = 90°, hence arc ED = arc EB − arc BD = 180° − 90° = 90°. With arc DC = 50°, arc EC = arc ED + arc DC = 90° + 50° = 140°. The arc EBC is the other (major) arc from E to C, so its measure is 360° − 140° = 220°.
Reason: EB is a diameter so arc EB = 180°. Angle BOD = 90° gives arc BD = 90°, hence arc ED = arc EB − arc BD = 180° − 90° = 90°. With arc DC = 50°, arc EC = arc ED + arc DC = 90° + 50° = 140°. The arc EBC is the other (major) arc from E to C, so its measure is 360° − 140° = 220°.
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