Q14 of 100 Page 17

In Fig. 16.186, O is the centre of the circle. If ∠CEA=30°, find the values of x, y and z.

We have,

∠AEC = 30o


Since, quadrilateral ABCE is a cyclic quadrilateral


Then,


∠BAC + ∠AEC = 180o


x + 30o= 180o


x = 150o


By degree measure theorem,


∠AOC = 2 ∠AEC


y = 2 * 30o


= 60o


Therefore,


∠ADC = ∠AEC (Angles in same segment)


z = 30o


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