Question

number of sectors that are formed will be equal to $\frac{360^{circ}}{n^{circ}}$. the arc - length of each sector is the circumference divided by the number of sectors, or ___. therefore, the arc length of a sector of a circle with a central angle of $n^{circ}$ is given by $2pi rcdot\frac{n}{360}$ or $\frac{pi rn}{180}$. a. $2pi rdiv\frac{270}{n}$ b. $2pi rdiv\frac{180}{n}$ c. $2pi rdiv\frac{90}{n}$ d. $2pi rdiv\frac{360}{n}$

Explanation:

Step1: Recall circle - arc length formula

The circumference of a circle is $C = 2\pi r$.

Step2: Understand arc - length relationship

If a circle is divided into $\frac{360}{n}$ sectors (where $n$ is the central - angle of each sector in degrees), and the arc - length of each sector $l$ is the circumference divided by the number of sectors. Let the number of sectors be $s=\frac{360}{n}$. Then $l = 2\pi r\div s=2\pi r\div\frac{360}{n}$.

Answer:

D. $2\pi r\div\frac{360}{n}$