How many Radians?

The perimeter of sector is $= \color{#EC7300}{\text{Radius + Radius + Arc Length}}$ . Since the radius is $4$ and the perimeter is $18$ , the arc length is $10$ . $\\ \begin{aligned} \text{Radian} &= \dfrac{\text{Length of arc}} {\text{Radius}} \\ \\ \text{Radian} &= \color{#EC7300}{\dfrac{10}{4}} \\ \\ \text{Radian} &= \boxed{2.5} \end{aligned}$

Let the angle of the sector be $\theta$ . Then the perimeter is given by:

$\begin{aligned} p & = \theta r + 2r \\ 18 & = 4\theta + 2(4) \\ \implies \theta & = \frac {10}4 = \boxed{2.5} \end{aligned}$