Question

the radius of a circle is 4 inches. what is the angle measure of an arc bounding a sector with area ( 2pi ) square inches?
give the exact answer in simplest form.

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(K=\frac{\theta}{360}\times\pi r^{2}\), where \(K\) is the area of the sector, \(\theta\) is the central angle in degrees, and \(r\) is the radius of the circle.

Step2: Substitute the given values into the formula

We are given that \(K = 2\pi\) square inches and \(r = 4\) inches. Substituting these into the formula:

$$
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$$

Step3: Solve for \(\theta\)

First, divide both sides of the equation \(2\pi=\frac{\theta}{360}\times16\pi\) by \(\pi\) (since \(\pi
eq0\)):

$$
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$$

Answer:

\(45\)