Question

In figure , find the values of X and Y if O is the centre of the circle.​

Answer 1

Answer:

x= 80, y=100

Step-by-step explanation:

angle at the centre is double to the angle at the circumference so angles AOB = 2*(angle ADB)

so 160 = 2x

2x=160

x= 160/2= 80

and ABCD is cyclic quadrilateral so opposite angles add up-to 180

x+y= 180

80+y= 180

y=180-80

y=100

Answer 2

Answer:

reflex <O = 360° - 160° = 200°

<Y = 1/2 of reflex <O [angle subtended by the centre is double the angle lying on the circle]

<Y = 1/2 × 200°

<Y = 100°

<X = 1/2 of <O [angle subtended by the centre is double the angle lying on the circle]

<X = 1/2 × 160°

<X = 80°