warm up problem 15: concentric circles easy.

Since all circles are similar, we can set up a proportion:

$\frac{\pi}{5}=\frac{4\pi}{x+5}$

$\pi x+5\pi=20\pi$

$x=15$

As per theorem , angle = arc/radius . so angle is same .then compare both angle .

(x/5)=(4x/(x+5)) x=15

By ratio and proportion, we have

$\dfrac{5}{\pi}=\dfrac{5+x}{4 \pi}$ $\implies$ $\dfrac{20 \pi}{\pi}=5+x$ $\implies$ $20-5=x$ $\implies$ $\color{#D61F06}\boxed{x=15}$