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