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Question
In the figure given alongside, AD is the diameter of the circle. If ∠ BCD = 130°, Calculate: (i) ∠ DAB (ii) ∠ ADB.
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Solution
(i) Since ABCD is a cyclic quadrilateral.
∴ Its Opposite angles are supplementary.
∴ ∠ DAB + ∠ BCD = 180°
⇒ ∠ DAB = 180° - ∠ BCD
⇒ ∠ DAB = 180° - 130°
⇒ ∠ DAB = 50°
(ii) Since, angle in the semicircle is a right angle.
∴ In Δ ABD, ∠ABD = 90°
Since, the sum of the angle of a triangle is 180°
∴ ∠ABD + ∠ADB + ∠ DAB = 180°
∴ 90° + ∠ADB + 50° = 180°
∠ADB = 180° - (90° + 50°)
∠ADB = 180° - 140°
∠ADB = 40°
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