Area of a Sector of a Circle Question

Question

In the figure, $AB$ and $CD$ are two arcs subtended at center $O$. $r$ is the radius of the sector $AOB$. I was told to find the radius, $x$ (the angle), and the shaded area. I know $2\pi r\cdot\dfrac x{360} = 13$. And $\pi(r+4)^2 \cdot \frac{x}{360} - \pi r^2 \cdot \frac{x}{360}$ = shaded area

Answer 1

Hint:

$$\begin{align}2\pi r\dfrac{x}{360} &= 13\tag{1}\\ 2\pi (r + 4)\dfrac x{360} &= 17\tag{2}\end{align}$$

What happens if you divide $(1)$ with $(2)$?

$$\begin{align}\dfrac{r}{r + 4} &= \dfrac{13}{17}\implies r = 13 \\ x = \dfrac{13\cdot360}{2\pi\cdot 13} &= \dfrac{180}{\pi}\end{align}$$

Answer 2

You are proceeding on the right path. I'll add one more equation as a hint: $$2π(r+4)\cdot \frac{x}{360}=?$$