Question

solomon needs to justify the formula for the arc length of a sector. which expression best completes this argument? the circumference of a circle is given by the formula c = πd, where d is the diameter. because the diameter is twice the radius, c = 2πr. if equally sized central angles, each with a measure of n°, are drawn, the number of sectors that are formed will be equal to ____. the arc length of each sector is the circumference divided by the number of sectors, or 2πr÷360/n. therefore, the arc length of a sector of a circle with a central angle of n° is given by 2πr·n/360 or πrn/180. a. 360°/n° b. 270°/n° c. 180°/n° d. 90°/n°

Explanation:

Step1: Recall circle angle property

The total angle around a circle is 360°.

Step2: Determine number of sectors

If each central - angle is \(n^{\circ}\), then the number of sectors formed is \(\frac{360}{n}\) since \(360\div n=\frac{360}{n}\).

Answer:

A. \(\frac{360^{\circ}}{n^{\circ}}\)