in circle g, gh = 10 and m∠hgi = 72°. find the length of (overparen{hi}). express your answer as a fraction times π (in simplest form).

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Accepted Answer

# Explanation:
## Step1: Recall the arc - length formula
The formula for the length of an arc $s$ of 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 the values of $\theta$ and $r$
Given that $\theta = m\angle HGI=72^{\circ}$ and $r = GH = 10$.
## Step3: Substitute the values into the formula
Substitute $\theta = 72^{\circ}$ and $r = 10$ into the formula $s=\frac{\theta}{360^{\circ}}\times2\pi r$.
$$
\begin{align*}
s&=\frac{72^{\circ}}{360^{\circ}}\times2\pi\times10\
&=\frac{72\times20\pi}{360}\
&=\frac{1440\pi}{360}\
& = 4\pi
\end{align*}
$$

# Answer:
$4\pi$

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Question

Explanation:

Step1: Recall the arc - length formula

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

Step3: Substitute the values into the formula

Answer: