A circle has a circumference of 6. It has an arc of length 1/3. What is The Central angle of the arc, in degrees?

Answer 1

Don't be afraid of fractions. A circle has 360 degrees. An arc will always be a ratio (expressed as a fraction over 360.

So your unknown angle projecting the arc is n/360 that will be equal to the 1/3 value over the 6. Think of two fractions stacked as one fraction 1/3 over 6/1. The rule is flip and multiply here. so 1/3 x 1/6 gives us 1/18.

so n/360 = 1/18. Since 360 is 18x20, your ratio will be n/360 = 20/360. So, the n value is 20 degrees.

Answer 2

central angle of the arc = 20 degrees.

The circumference of a circle subtends 360 degrees

The length of an arc subtends a fraction of 360 degrees depending on the length of the arc.

This is a ratio problem.

θ/360 = (1/3)/6

θ = 20