Q. 144.3( 4 Votes )

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

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}

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