The diameter of a circle is 10 feet. What is the angle measure of an arc bounding a seci with area \( 10 \pi \) square feet?
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Answer

4. Use ratio to find the angle measure of sector: \( \theta \) = \( \frac{2}{5}(360) \) = 144 degrees.

Steps

Step 1 ：1. Find radius: r = \( \frac{d}{2} \) = \( \frac{10}{2} \) = 5

Step 2 ：2. Find circle area: A_c = \( \pi r^2 \) = \( \pi (5)^2 \) = 25\pi

Step 3 ：3. Find the ratio of the sector area to the circle area: \( \frac{A_s}{A_c} \) = \( \frac{10\pi}{25\pi} \) = \( \frac{2}{5} \)

Step 4 ：4. Use ratio to find the angle measure of sector: \( \theta \) = \( \frac{2}{5}(360) \) = 144 degrees.