Answer:
40°
Step-by-step explanation:
In any circle the following ratios are equal
let x be the measure of the central angle, then
[tex]\frac{arc}{circumference}[/tex] = [tex]\frac{x}{360}[/tex]
circumference = 2πr = 2π × 18 = 36π, so
[tex]\frac{4\pi }{36\pi }[/tex] = [tex]\frac{x}{360}[/tex], that is
[tex]\frac{1}{9}[/tex] = [tex]\frac{x}{360}[/tex] ( cross- multiply )
9x = 360 ( divide both sides by 9 )
x = 40
Hence central angle = 40°
