Mathematics
In the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.
Circles
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Answer
We know that,
Angle at the center is double the angle at the circumference subtended by the same chord.
∠AOC = 2∠ABC = 2 × 55° = 110°.
∴ x = 110°.
ABCD is a cyclic quadrilateral.
∴ ∠ADC + ∠ABC = 180°
⇒ y + 55° = 180°
⇒ y = 180° - 55° = 125°.
Hence, x = 110° and y = 125°.
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