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Question
In figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).
Solution
Chords AC and DE intersect internally at point B.
∴ ∠ABE = `1/2` [m(arc AE) + m(arc DC)]
∴ 108° = `1/2` [95° + m(arc DC)]
∴ 108° × 2 = 95° + m(arc DC)
∴ 95° + m(arc DC) = 216°
∴ m(arc DC) = 216° − 95°
∴ m(arc DC) = 121°
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