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Question
In cyclic quadrilateral ABCD, ∠DAC = 27°; ∠DBA = 50° and ∠ADB = 33°.
Calculate:
- ∠DBC,
- ∠DCB,
- ∠CAB.
Solution
i. ∠DBC = ∠DAC = 27°
(Angle subtended by the same chord on the circle are equal)
ii. ∠ACB = ∠ADB = 33°
∠ACD = ∠ABD = 50°
(Angle subtended by the same chord on the circle are equal)
∴ ∠DCB = ∠ACD + ∠ACB
= 50° + 33°
= 83°
iii. ∠DAB + ∠DCB = 180°
(Pair of opposite angles in a cyclic quadrilateral are supplementary)
`=>` 27° + ∠CAB + ∠83° = 180°
`=>` ∠CAB = 180° – 110° = 70°
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