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 , where d is the diameter.Because the diameter is twice the radius, .If equally sized central angles, each with a measure of , 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 .Therefore, the arc length of a sector of a circle with a central angle of is given by or ... help please

Answer 1

Answer:

$\frac{360}{n}$

Step-by-step explanation:

Given:

The above statements

Required

Complete the above statements

Considering the third statement in the question;

First, it should be noted that a circle is a full sector that measures 360 degrees

Assuming the circle is divided by a central angle of 180, the number of sectors formed will be;

$\frac{360}{180} = 2\ sectors$

Further assume the circle is divided by a central angle of 90, the number of sectors formed will be;

$\frac{360}{90} = 4\ sectors$

Similarly, if the circle is divided by a central angle of n, the number of sectors formed will be;

$\frac{360}{n}$

Hence, from the list of given options; $\frac{360}{n}$ fills the gap correctly