Respuesta :
The measure of the central angle of the arc of a circle which has a circumference of 8. It has an arc of length 32/5 is 288 degrees.
What is the central angle of the arc?
Central angle is the angle which is substended by the arc of the circle at the center point of that circle.
The formula which is used to calculate the central angle of the arc is given below.
[tex]\theta=\dfrac{s}{r}[/tex]
Here, (r) is the radius of the circle, (θ) is the central angle and (s) is the arc length.
A circle has a circumference of 8. The circumference of the circle is 2π times the radius of the circle. Thus, the radius of the circle is,
[tex]8=2\pi r\\r=\dfrac{8}{2\pi}\\r=1.273\rm\; units[/tex]
It has an arc of length 32/5. Thus the centeral angle is,
[tex]\theta=\dfrac{\dfrac{32}{5}}{1.273}\\\theta=5.023\rm rad[/tex]
Convert it into the degree by multiplying with 180/π.
[tex]\theta=5.023\times\dfrac{180}{\pi}\\\theta=288^o[/tex]
Thus, the measure of the central angle of the arc of a circle which has a circumference of 8. It has an arc of length 32/5 is 288 degrees.
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