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Question
In the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.
Solution
∠AOC = 2∠ABC = 2 × 55°
(Angle at the centre is double the angle at the circumference subtended by the same chord)
∴ x = 110°
ABCD is cyclic quadrilateral
∴ ∠ADC + ∠ABC = 180°
(Pair of opposite angles in a cyclic quadrilateral are supplementary
`=>` y = 180° – 55° = 125°
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