a circle has a circumfernce of 6. It has an arc length of 1

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a circle has a circumfernce of 6. It has an arc length of 1

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2 weeks 2021-11-14T00:01:39+00:00 1 Answer 0 views 0

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°