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

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

Since, angle in the same segment are equal

So

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

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°