Let the central angle subtended by two points on a circle is 120°. Then the inscribed angle subtende

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Let the central angle subtended by two points on a circle is 120°. Then the inscribed angle subtended by those points is ________.

Accepted Answer

{"content":[{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Inscribed Angle Theorem):","type":"text"},{"type":"text","text":" The Inscribed Angle Theorem states that the angle subtended by an arc at any point on the circle (the inscribed angle) is exactly half of the angle subtended by the same arc at the center of the circle (the central angle)."}]},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Direct Calculation):","type":"text"},{"text":" We are given that the central angle is ","type":"text"},{"attrs":{"latex":"120^\circ"},"type":"math_inline"},{"text":". Using the theorem:","type":"text"}]},{"attrs":{"latex":"\text{Inscribed Angle} = \frac{1}{2} \times \text{Central Angle}"},"type":"math_block"},{"type":"math_block","attrs":{"latex":"\text{Inscribed Angle} = \frac{120^\circ}{2} = 60^\circ"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The inscribed angle is exactly ","type":"text"},{"attrs":{"latex":"60^\circ"},"type":"math_inline"},{"text":". The numeric value is ","type":"text"},{"text":"60","type":"text","marks":[{"type":"code"}]},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

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