The movement of the ant illustrates the length of an arc
The measure of the central angle is 2.625 radians
How to determine the central angle
The radius of the arc is given as:
[tex]r = 8[/tex]
The distance walked is given as:
[tex]L = 21[/tex]
The length of an arc is
[tex]L = r\theta[/tex]
So, we have:
[tex]21 = 8\theta[/tex]
Divide both sides by 8
[tex]\theta = \frac{21}{8}[/tex]
Divide
[tex]\theta = 2.625[/tex]
Hence, the measure of the central angle is 2.625 radians
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