I'm not sure what you want here.  But I'll do enough of it to get you
so you can finish.

Let AB be the chord which divides the area of the circle so that
the area above AB is 1/3 of the area of the circle .
Then the area below AB will be 2/3 of the area of the circle. Then
they will be in the ratio 1:2



We draw in two radii to A and B.



First we find the area of the sector AOB ("piece of pie") 



In this case, 



We must subtract the area of triangle AOB to get the area
above AB.

If a triangle has two sides with lengths x and y, and the 
angle between these two sides is θ degrees, then the area 
of the triangle is given by the equation 



In this case, x and y both equal the radius r, and 




The area above AB is



This must equal 1/3 of the area, which is  

So the equation is 

 

We divide through by r2



You can only solve that for  with technology.

I used a TI-84 Plus.  I got 149.27417o

Use that to find whatever else your teacher wants. 

Edwin