Question

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

Answer 1

We have, 

∠AEC = 30° 

Since, 

quadrilateral ABCE is a cyclic quadrilateral 

Then, 

∠BAC + ∠AEC = 180° 

x + 30° = 180° 

x = 150° 

By degree measure theorem, 

∠AOC = 2 

∠AEC 

y = 2 x 30° = 60° 

Therefore, 

∠ADC = ∠AEC 

(Angles in same segment) 

z = 30°