Question

1. 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, $r$. a $r = \frac{360cdot l_a}{2pi x}$ b $r=\frac{360cdot l_a}{2pi}$ c $r=\frac{2pi xcdot l_a}{360}$ d $r=\frac{360}{2pi x}$

Explanation:

Step1: Start with the given formula

$L_a=\frac{x}{360}\cdot 2\pi r$

Step2: Isolate $r$

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

Answer:

A. $r=\frac{360\cdot L_a}{2\pi x}$