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The formula for finding the length of an arc on a circle is L=2πr(x/360), where r is the radius of the circle and x is the measure of the central angle of the arc.
Solve for x.
x=Lπr/180
x=180L/πr
x=L/720πr
x=720πr/L

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Answer:

x = 180L/πr

Step-by-step explanation:

Step 1: Write equation

L = 2πr(x/360)

Step 2: Isolate x term (Divide both sides by 2πr)

L/(2πr) = x/360

Step 3: Multiply both sides by 360

360L/(2πr) = x

Step 4: Simplify

180L/πr = x

x = 180L/πr

chasiaaaa

Step-by-step explanation:

The formula for length of an arc on a circle is given by the formula:

L = \frac{2 \pi rx}{360}L=

360

2πrx

,

where 'r' is the radius of the circle and 'x' is the measure of the central angle of the arc.

We have to determine the value of radius 'r'.

Since, L = \frac{2 \pi rx}{360}L=

360

2πrx

By Cross multiplication, we get

360 \times L = 2 \pi rx360×L=2πrx

\frac{360 \times L}{ 2 \pi x} =r

2πx

360×L

=r

\frac{180 \times L}{ \pi x} =r

πx

180×L

=r

r = \frac{180L}{ \pi x}r=

πx

180L

Therefore, the radius 'r' is given by r = \frac{180L}{ \pi x}r=

πx

180L

.

Option 4 is the correct answer .

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