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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?

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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