in circle k, kl = 9 and m∠lkm = 80°. find the length of $\overarc{lm}$. express your answer as a fraction times π (in simplest form).

Question

Accepted Answer

# Explanation:
## Step1: Recall arc length formula
The formula for the length of an arc $ s $ in a circle is $ s=\frac{\theta}{360^\circ}\times2\pi r $, where $ \theta $ is the central angle in degrees and $ r $ is the radius of the circle.
## Step2: Identify values of $ \theta $ and $ r $
Here, the central angle $ \theta = m\angle LKM = 80^\circ $, and the radius $ r = KL = 9 $ (since $ KL $ is a radius of circle $ K $).
## Step3: Substitute values into the formula
Substitute $ \theta = 80^\circ $ and $ r = 9 $ into the arc length formula:
$$
\begin{align*}
s&=\frac{80^\circ}{360^\circ}\times2\pi\times9\
&=\frac{80}{360}\times18\pi\
&=\frac{2}{9}\times18\pi\
& = 4\pi
\end{align*}
$$

# Answer:
$ 4\pi $

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QUESTION IMAGE

Question

Explanation:

Step1: Recall arc length formula

Step2: Identify values of \( \theta \) and \( r \)

Step3: Substitute values into the formula

Answer: