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Question
In the figure given alongside, AB and CD are straight lines through the centre O of a circle. If ∠AOC = 80° and ∠CDE = 40°, find the number of degrees in:
- ∠DCE,
- ∠ABC.
Solution
i. Here, ∠CED = 90°
(Angle in a semicircle is a right angle)
∴ ∠DCE = 90° – ∠CDE
= 90° – 40°
= 50°
∴ ∠DCE = ∠OCB = 50°
ii. In ΔBOC,
∠AOC = ∠OCB + ∠OBC
(Exterior angle of a Δ is equal to the sum of pair of interior opposite angles)
`=>` ∠OBC = 80° – 50° = 30° ...[∠AOC = 80°, given]
Hence, ∠ABC = 30°
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