Question

In the diagram, point O is the center of the circle. If
m∠ABC = 70°, what is m∠AOC ?

Answer 1

Explanation:

Alright, lets get started.

Please refer the diagram I have attached.

Let us suppose angle ABO = x and angle CBO = y, so,

`x+y=70`

AO and BO will be same as both are radius.

Similarly, CO nd BO will be same as both are radius.

angle AOB =
`180-x-x=180-2x`

angle COB =
`180-y-y=180-2y`

Angle AOC =
`360-(AOB+COB)=360-(180-2x+180-2y)=360-360+2(x+y)`

Angle AOC =
`2(x+y)`

Putting the value of (x+y) as 70, then

`Angle AOC = 2*70=140`

So te answer is 140° : Answer

Hope it will help :)