Answer:
m∠FAN = 80°
Step-by-step explanation:
Area of a sector is given by the expression,
Area of the sector = [tex]\frac{\theta}{360}\pi r^{2}[/tex]
Here, θ = central angle subtended by the arc
r = Radius of the circle
By substituting the values from the question,
288π = [tex]\frac{\theta}{360}(\pi )(36)^2[/tex]
θ = [tex]\frac{288\pi }{1296\pi }\times 360[/tex]
θ = 80°
Therefore, m∠FAN = 80° will be the answer.
