The diameter of a circle is 10 miles. What is the angle measure of an arc bounding a sector with area 10 square miles?

Answer: the angle measure of the arc bounding a sector is 45.86 degrees

Step-by-step explanation:

The formula for determining the area of a sector is expressed as

Area of sector = θ/360 * πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Diameter = 10 miles

Radius = diameter/2 = 10/2 = 5 miles

Area of sector = 10 square miles

Therefore,

10 = θ/360 * 3.14 * 5²

10 = θ/360 * 78.5

78.5θ = 10 * 360 = 3600

θ = 3600/78.5

θ = 45.86 degrees