In Figure, `O` is the centre of the circle. If `/_C E A=30^0,` find the values of `x ,\ y\ a n d\ z`

Explanation

`/_C E A=30^0`(Given)
Since angles in same segment are equal.
`/_AEC=/_ADC=30^0`
`z=30^0`...(i)
`ABCE` is cyclic quadrilateral
`/_AEC+/_ABC=180^0`(sum of opposite angles )
`30^0+/_ABC=180^0`(from (i))
`x=150^0`
central angle is twice the inscribed angle that enclosed the same arc
`/_AYC=2/_AEC`
`y=2xx30^0`
`y=60^0`