ABC is a triangle inscribed in a circle with center O. If angle AOC = 130 and angle BOC = 150, find angle ACB.

In triangle AOC,

AO = OC    (radii of same circle)

.^.., angle OCA=angle OAC,

Now, angle AOC = 130^o

So, angle OCA=angle OAC =(180-130) / 2 = 25⁰
 

Follow the same steps in triangle OBC.

You will get angle OCB =15⁰ .

Now add angle ACO and angle OCB = 25 +15 = 40⁰.

Hope this helps!

Cheers,

Rishab