In the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.
∠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°
Solution In the Given Figure, O is the Centre of the Circle and ∠Abc = 55°. Calculate the Values of X and Y. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.