a circle has a circumference of 6. It has an arc of length 1. What is the central angle of the arc, in degrees?

Answer 1

The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:

6= πd and then divide both sides of the equation by π you get that d = 1.90

To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:

1 = 0.9549θ.

If you divide both sides of the equation by 0.9549 you get θ = 1.047197 radians.

The question asked for the angle measure in degrees so you would need to convert the angle measure to degrees by multiplying the degree measurement by 180/π

1.047197 x 180/π = 60°

Answer 2

circumference = 6 = 2πr. so r = 6/2π

arc length = rθ. 1 = (6/2π)θ. so θ = 2π/6 = π/3. convert to degrees by multiplying by 180/π

π/3 x 180/π = 60 deg