Answer:
[tex] \blue{ \theta = 72 \degree }[/tex]
Step-by-step explanation:
The formula to find length of an arc is :
[tex]arc \: \: length \: = \frac{ \theta}{360} \times 2\pi \: r[/tex]
Here,
[tex]arc \: \: length = 4\pi \\ r = radius = 10ft \\ [/tex]
[tex] \red{\theta = } \red{measure \: of \: the \: angle}[/tex]
We can solve for measure of the angle of the arc by using the above formula.
Let us solve now.
[tex]arc \: \: length \: = \frac{ \theta}{360} \times 2\pi \: r \\ 4\pi= \frac{ \theta}{360} \times 2\pi \: \times 10 \\ 4\pi = \frac{ \theta}{360} \times 20\pi \\ 360 \times 4\pi = 20 \pi\theta\\ 1440\pi = 20\pi \theta \\ \frac{1440\pi}{20\pi} = \frac{20\pi \theta}{20\pi} \\ 72 \degree = \theta[/tex]
