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In the given figure, *O* is the centre of the circle. If ∠*CEA* = 30°, Find the values of *x*, *y* and *z*.

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#### Solution

It is given that, *O* is the centre of the circle and `angle AEC = 30°`

We have to find the value of *x*, *y* and *z*.

Since, angle in the same segment are equal

So `angle AEC = angle ADC = 30°`

And *z* = 30°

As angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Since `angle AOC = 2 angle ADC`

Then,*y *= 2*z*

= 2 × 30°

= 60°

Since, the sum of opposite pair of angles of a cyclic quadrilateral is 180°.*z* + *x* = 180°*x *= 180° − 30°

= 150°

Hence,*x* = 150°, *y* = 60° and *z* = 30°

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