Here is an other approach to your question:

1. You are dealing with a right triangle even though you can't see it (compare my sketch)

2. In a right triangle you know that

and

3. Since you already know x = 6 and s = 24 you have to solve for r:

4. The central angle of the sector which contains the segment as a "cap" is:

and

5. I'll leave the rest for you.