Question

In the figure, O is the centre of the circle. If $\angle CEA={30}^o$, find the values of x, y and z.

Answer 1

$\angle AECand\angle ADC$ are in the same segment .

$\therefore \angle AEC=\angle ADC={30}^o$

$\therefore z={30}^o$

ABCD is a cyclic quadrilateral.

$\therefore \angle B+\angle D={180}^o$

$\Rightarrow x+z={180}^o$

$\Rightarrow x+{30}^o={180}^o\Rightarrow x={180}^o-{30}^o={150}^o$

Arc AC subtends $\angle AOC$ at the centre and $\angle ADC$ at the remaining part of the circle.

$\therefore \angle AOC=2\angle D=2\times {30}^o={60}^o$

$\therefore y={60}^o$

Hence, $x={150}^o,y={60}^{o}andz={30}^o$