Question

in fig o is the center find x and y​

Answer 1

We know that angle subtended by an arc of a circle at the centre is double the angle subtended by it on remaining part of the circle. Arc CD subtends ∠COD at centre and subtends ∠BCD at B on the circle .

Hence ∠COD = 2∠BCD

That is ∠COD = 2y [Since ∠BCD = y] Also ∠COD = ∠OCB = 30° [Alternate angles] That is 2y = 30°

Therefore, y = 15° From the figure ∠AOD = 90° since ∠AEB = ∠AEC = 90°

Therefore, ∠AOD = 2∠ABD That is 90° = 2∠ABD

Hence ∠ABD = 45° In ΔAEB, ∠AEB + x + y + 45° = 180°

90°+ x + 15°+ 45° = 180°

x = 180° - 150° = 30°