Question

In the adjacent figure find x and y when given that O is the centre of the circle​

Answer 1

b'

Given information: O is the center of the circle.

According to the central angle theorem, the angle subtended by an arc is always half of its central angle.

Let the Central angle of arc AB is 70∘

.

∠ACB and ∠ADB are subtended by the arc AB.

∠ACB=∠ADB=  

2

70∘

 

​  

=35∘

 

∴x=y=35∘

b'

Given information: O is the center of the circle.

According to the central angle theorem, the angle subtended by an arc is always half of its central angle.

Let the Central angle of arc AB is 70  

∘

.

∠ACB and ∠ADB are subtended by the arc AB.

∠ACB=∠ADB=  

2

70  

∘

 

​  

=35  

∘

 

∴x=y=35  

∘

Answer 2

Given : O is the centre of the circle

To Find : x and y

Solution:

O is the center of circle

=> BD is diameter

Hence ∠BAD = 90°

∠BAD = 75° + x

=> 75° + x = 90°

=>  x = 15°

∠ADB + 90° + 35° = 180°  ( sum of angles of triangle )

=> ∠ADB  =55°

∠ACB  =  ∠ADB   ( angle by same arc AB)

=>  ∠ACB  =55°

=> y = 55°

x = 15° and y = 55°

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