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

Question

In Fig. 16.186, O is the centre of the circle. If &#x2220; CEA =30&#xB0;, find the values of x, y and z .

Philoid · Accepted Answer

We have,

∠AEC = 30^o

Since, quadrilateral ABCE is a cyclic quadrilateral

Then,

∠BAC + ∠AEC = 180^o

x + 30^o= 180^o

x = 150^o

By degree measure theorem,

∠AOC = 2 ∠AEC

y = 2 * 30^o

= 60^o

Therefore,

∠ADC = ∠AEC (Angles in same segment)

z = 30^o