Question

In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of xand 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 `angle A + angle C = 180°` 

So,

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

Clearly  Δ OAB is an isosceles triangle with OA = OB and  `angle OBA = angle OAB`

Then,  `angle OBA + angleOAB + angle AOB = 180°` 

`angleAOB = 180° - ( 50° + 50° ) `          (Since `angleOBA = angle OAB = 50°` )

So, `angleAOB = 80°`

x +  `angle AOB ` = 180°     (Linear pair)

Therefore, x =  180° − 80° = 100°

Hence,

 x = 100°  and  y = 130°