Centrzl angle of the arc

Question

A circle has a circumference of 18, It has an arc length of 6

Whats the central angle of the arc in degrees?

Answer 1

Circumference formula C=πd 

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:

18= πd and then divide both sides of the equation by π you get that d = 5.73 

r=1/2(d) = (1/2)(5.73) = 2.86

To find the central angle of an arc you would use the equation: S = rθ 

S is the length of the arc 

r is the radius of the circle

θ is the measure of the angle which in this case is unknown.

So with S = 6 and r = 2.86 you would have an equation that looks like this:

6 = 2.86θ. 

If you divide both sides of the equation by 2.86 you get θ = 2.09 radians. 

Now convert the angle measure to degrees by multiplying the degree measurement by 180/π

2.09 x 180/π = 120°

Circumference formula C=πd 

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:

18= πd and then divide both sides of the equation by π you get that d = 5.73 

r=1/2(d) = (1/2)(5.73) = 2.86

To find the central angle of an arc you would use the equation: S = rθ 

S is the length of the arc 

r is the radius of the circle

θ is the measure of the angle which in this case is unknown.

So with S = 6 and r = 2.86 you would have an equation that looks like this:

6 = 2.86θ. 

If you divide both sides of the equation by 2.86 you get θ = 2.09 radians. 

Now convert the angle measure to degrees by multiplying the degree measurement by 180/π

2.09 x 180/π = 120°

Answer 2

The arc is 1/3 of the circumference, 6/18 = 1/3.

Therefore the central angle is 1/3 of 360° or 120º