Answer:
45 .85° degree measure of the arc of the sector.
Step-by-step explanation:
Given : In a circle of radius 10 cm, a sector has an area of 40 sq. Cm.
To find : What is the degree measure of the arc of the sector
Solution : We have given that
Radius = 10 cm.
Area of sector = 40 sq. Cm.
Area of sector = [tex]\frac{theta}{360} * \pi (radius)^{2}[/tex].
Plug the values
40 = [tex]\frac{theta}{360} * 3.14 (10)^{2}[/tex].
40 = [tex]\frac{theta}{360} * 3.14 (100)[/tex].
40 = [tex]\frac{theta}{360} * 314[/tex].
On multiplying by 360 both sides
40 * 360 = theta * 314
14400 = Theta * 314 .
On dividing both side by 314
Theta = 45 .85°
Therefore, 45 .85° degree measure of the arc of the sector.
