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A circle has a circumference of 12. It has an arc of length 8/5. what is the central angle of the arc, in degrees?

 Mar 4, 2020
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So lets start out by figuring out what fraction of the whole circumference the arc takes up.

 

The arc has a length of \(\frac{8}{5}\), or \(1.6\), out of a circle with circumference \(12\).

 

The arc takes up \(\frac{1.6}{12} = \frac{16}{120} = \frac{2}{15}\)of the whole circumference. 

 

This also means that the central angle of the arc takes up \(\frac{2}{15}\) of the entire \(360\) degree angle.

 

So the central angle of the arc is \(\frac{2}{15}\) of \(360\), which is \(\boxed{48 \space \text{degrees}}\).

 Mar 4, 2020

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