Question

In the given figure, O and O' are centres of two circles intersecting at B and C. ACD is a straight line, find x. 

 

Answer 1

It is given that

Two circles having center O and O' and ∠AOB = 130°

And AC is diameter of circle having center O 

We have

`angle ACB =1/2 angleAOB = 65°`

So

`angleDCB = 180° - angleACB`

                  = 180° - 65°

                 = 115°

Now, reflex `angleBO'D = 2 angleBCD` 

So

`360° - x° = 2 xx 115 `

                = 230° 

           x° = 360° - 230° = 130°

Hence, x = 130°