Question

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

 

Answer 1

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 = 2z
   = 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°