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Find the measure of the central angle.

the circle has a circumference of 9 and the arc length is 1. Use 3.14 for pie.

Verified Answer :

To start with we have to write down what we know. pi=3.14, r=9, arc length is 1. x is the angle we are trying to find. Saying that the radius is 9

There is an equation that states that the arc length is equal to x/360 (the fraction of the circle) multiplied by the circumference or 2 times pi times the radius.
\(L= \frac{x}{360} * 2 \pi r\)
where * means multiply.
\(1= \frac{x}{360} * 3.14 * 9\)
Simplify
\(1= \frac{x}{360} *28.26\)
Take the 28.26 over to the other side of the equation, where it then it divides the 1.
\(\frac{1}{28.26} = \frac{x}{360}\)
This becomes: \(0.035= \frac{x}{360}\)
Then the 360 is brought over to the other side and multiplies the 0.035:
\(360*0.035=x\)
And finally simplify the whole equation and we get our answer.
\(x=12.739 degrees x=12.7 degrees\)

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