Chords AB and CD of a circle intersect at point E inside the circle. If m(arc AC) = 80^° and m(arc BD) = 50^°, find m∠ AEC and m∠ CEB. [Figure: chords AB and CD cross at E; arc AC and arc BD are the arcs opposite each other, intercepted by ∠ AEC and ∠ BED .]

Answer: m∠ AEC = 65^°, m∠ CEB = 115^° m∠ AEC = 1/2[m(arc AC) + m(arc BD)] (angle between chords intersecting inside the circle) = 1/2(80^° + 50^°) = 65^°. ∠ AEC and ∠ CEB form a linear pair, so m∠ CEB = 180^° - 65^° = 115^°.

Chapter: Circle· Mathematics Part 2 (Geometry)

Chords AB and CD of a circle intersect at point E inside the circle. If \(m(\text{arc } AC) = 80^\circ\) and \(m(\text{arc } BD) = 50^\circ\), find \(m\angle AEC\) and \(m\angle CEB\).[Figure: chords AB and CD cross at E; arc AC and arc BD are the ar…

Chords AB and CD of a circle intersect at point E inside the circle. If \(m(\text{arc } AC) = 80^\circ\) and \(m(\text{arc } BD) = 50^\circ\), find \(m\angle AEC\) and \(m\angle CEB\).

[Figure: chords AB and CD cross at E; arc AC and arc BD are the arcs opposite each other, intercepted by \(\angle AEC\) and \(\angle BED\).]

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Answer: \(m\angle AEC = 65^\circ\), \(m\angle CEB = 115^\circ\)

\(m\angle AEC = \dfrac{1}{2}\left[m(\text{arc } AC) + m(\text{arc } BD)\right]\) (angle between chords intersecting inside the circle) \(= \dfrac{1}{2}(80^\circ + 50^\circ) = 65^\circ\).

\(\angle AEC\) and \(\angle CEB\) form a linear pair, so \(m\angle CEB = 180^\circ - 65^\circ = 115^\circ\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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Chords AB and CD of a circle intersect at point E inside the circle. If \(m(\text{arc } AC) = 80^\circ\) and \(m(\text{arc } BD) = 50^\circ\), find \(m\angle AEC\) and \(m\angle CEB\).[Figure: chords AB and CD cross at E; arc AC and arc BD are the ar…

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