Question

Find the value of x and y from the circle with centre ‘O’ where

∠ACB = 65°, ∠OAB = x and ∠AOB = y.
​

Answer 1

Answer:

Given,

(i)∠AOC=100

o

Now,

∠AOC+∠BOC=180

o

=>∠BOC=180

o

−100

o

=80

o

Now,

we know that the angle at the centre is twice the angle at the

circumference subtended by the same arc.

Therefore,

∠BDC=

2

1

∠BOC

=(

2

1

×80

o

)

=40

o

(ii)Given,

O is the centre of the circle.

∠AOD=40

o

and ∠BDC=100

o

Now,

we know that the angle at the centre is twice the angle at the

circumference subtended by the same arc.

Therefore,

∠ABC=

2

1

∠AOC

=(

2

1

×40

o

)

=20

o

In △BCD

∠DBC+\angle BDC+∠DCB=180[sum of all angle of △]

=>20

o

+100

o

+∠DCB=180

o

=>∠DCB=60

o

=>∠OCB=60

o