Question

question 1 - 7
the arc length ($l_a$) of a sector of a circle with angle measure $x$ (in degrees) and radius $r$, is given by the equation $l_a=\frac{x}{360}cdot2pi r$.
solve the equation for the radius of the sector, $r$.
$r = \frac{360cdot l_a}{2pi x}$
$r=\frac{360cdot l_a}{2pi}$
$r=\frac{2pi x}{360}cdot l_a$
$r=\frac{l_a-\frac{x}{360}}{2pi}$

Explanation:

Step1: Start with given formula

$L_a=\frac{\theta}{360}\cdot2\pi r$

Step2: Isolate $r$

First, multiply both sides by $\frac{360}{\theta}$ to get $\frac{360L_a}{\theta}=2\pi r$.
Then divide both sides by $2\pi$: $r = \frac{360L_a}{2\pi\theta}$

Answer:

$r=\frac{360\cdot L_a}{2\pi\theta}$ (corresponding to the first - option in the multiple - choice list if we assume $\theta$ is represented by $x$ in the options)