MHB Can you find x using the trigonometry of circle sectors?

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I need help in solving this problem. Below shows all the measurements of the diagram, I need to find x:View attachment 6590
 

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For a circular sector of radius $r$, subtending angle $\theta$, the arc-length $s$ is given by:

$$s=r\theta$$

Can you apply this formula to get two equations in $x$ and $\theta$?

Or, we can use similarity to equate the ratio of radius to arc-length for both sectors. ;)
 

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