Question

In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of x and y.

Answer 1

It is given that, O is the centre of the circle and $\angle DAB=50°$.

We have to find the values of x and y.

ABCD is a cyclic quadrilateral and

So,

50° + y = 180°
y = 180° − 50°
y = 130°

Clearly is an isosceles triangle with OA = OB and

Then,

(Since)

So,

x + $\angle AOB$ = 180° (Linear pair)

Therefore, x = 180° − 80° = 100°

Hence,

and