A circle has a circumference of 6. it has an arc lengh of 1. what is the centeral angle of the arc in degrees

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

1.047197 x 180/π =  60°

Step-by-step explanation:

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°

question:

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