Question

In the figure, O is the centre of the circle and $\angle DAB={50}^o$. Calculate the values of x and y.

Answer 1

In the figure, O is the centre of the circle and $\angle DAB={50}^o$.

$\because ABCD$ is a cyclic quadrilateral,

$\therefore \angle A+\angle C={180}^o$

$\Rightarrow {50}^o+y={180}^o\Rightarrow y={180}^o-{50}^o={130}^o$

In $\Delta OAB$, OA = OB (Radii of the circle)

$\therefore \angle OAB=\angle OBA={50}^o$

Now, $\angle DOB=\angle OAB+\angle OBA$

$\Rightarrow x={50}^o+{50}^o={100}^o$

$\therefore x={100}^o,y={130}^o$