Question

question 1 - 7
the arc length (lₐ) of a sector of a circle with angle measure x (in degrees) and radius r, is given by the equation lₐ = 360/x • 2πr.
solve the equation for the radius of the sector, r.
○ r = 360/2πr • lₐ
○ r = 360 • lₐ/2π
○ r = 2πx/360 • lₐ
○ r = lₐ - x/360/2π

Explanation:

Step1: Write the formula for arc length

The formula for arc length \( L_{a}=\frac{x}{360}\cdot2\pi r \).

Step2: Solve for \( r \)

Multiply both sides by \( \frac{360}{2\pi x} \).
\( r=\frac{360\cdot L_{a}}{2\pi x} \).

Answer:

\( r=\frac{360\cdot L_{a}}{2\pi x} \)