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Question
ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°; calculate :
- ∠DAB,
- ∠BDC.
Solution
i. ∠DAB = ∠BED = 65°
(Angle subtended by the same chord on the circle are equal)
ii. ∠ADB = 90°
(Angle in a semicircle is a right angle)
∴ ∠ABD = 90° – ∠DAB = 90° – 65° = 25°
AB || DC
∴ ∠BDC = ∠ABD = 25° (Alternate angles)
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