Respuesta :
Answer:6
Step-by-step explanation:
120/360=.33333
.333333x18
The central angle of the arc, whose arc of length is 6 and the circle for this arc has circumference of 18 units, is 120 degrees.
What is the central angle of the arc?
The central angle is the angle which is subtended by the arc of the circle at the centre 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.
The circumference of the circle is 18. The circumference of the circle is 2π times the radius of it. Thus,
[tex]18=2\pi r\\r=\dfrac{18}{2\pi}[/tex]
The value of arc of length is 6,
[tex]s=6[/tex]
Put these values in the above formula,
[tex]\theta=\dfrac{6}{\dfrac{18}{2\pi}}\\\theta=\dfrac{6\times 2\pi}{18}\\\theta=\dfrac{ 2\pi}{3}\rm\; rad[/tex]
Multiply it with 180/π to convert it into degree.
[tex]\theta=\dfrac{ 2\pi\times180}{3\times\pi}\\\theta=120[/tex]
Thus, the central angle of the arc whose arc of length is 6 and the circle for this arc has circumference of 18 units, is 120 degrees.
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