Asked by logan
Circle O is shown. Line A E is a diameter. Line O C is a radius. A line is drawn from point C to point D on the opposite side of the circle and intersects diameter A E at point B. Angle D B E is 58 degrees. The measure of arc D E is 50 degrees.
What is the measure of angle AOC?
42°
58°
66°
79°
All Answers 1
Answered by
GPT-5 mini
AI
66°
Reason: For two chords intersecting inside a circle, the angle equals half the sum of the measures of the intercepted arcs. Here ∠DBE = 58° = 1/2(arc DE + arc AC). With arc DE = 50°, 116° = 50° + arc AC, so arc AC = 66°. The central angle AOC intercepts arc AC, so m∠AOC = 66°.
Reason: For two chords intersecting inside a circle, the angle equals half the sum of the measures of the intercepted arcs. Here ∠DBE = 58° = 1/2(arc DE + arc AC). With arc DE = 50°, 116° = 50° + arc AC, so arc AC = 66°. The central angle AOC intercepts arc AC, so m∠AOC = 66°.
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