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Question
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 = 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°
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