A circle has a circumference of 20. It has an arc of length 4. What is the central angle of the arc, in degrees?

Answer 1

If the circumference is 20, we can plug that into the equation C=2πr to find radius. C is circumference, r is radius.

20=2πr

r=10/π

(or r = 3.183 if you want to multiply it out)

Then you can take that radius and plug it into the arc length formula s=θr, where s is the length of the arc and r is the radius.

s=θr

4=θ(10/π)

4π/10=θ

2π/5=θ

Remember, that answer is in radians. If you need to convert that to degrees, multiply that angle by 180/π.

Hope this helps!

Answer 2

If you've had the equation L = C(θ/360) then you can solve for theta.

4 = 20 ( θ/360)

θ = 4(360)/20 = 72°

Answer 3

The setup for the given problem is as follows:

4/20=x/360°

Solving for x by multiplying by 360° will give us an answer of 72°.