Question

Central angle measure

Answer 1

40°

Explanation:

In any circle the following ratios are equal

let x be the measure of the central angle, then

`(arc)/(circumference)` =
`(x)/(360)`

circumference = 2πr = 2π × 18 = 36π, so

`(4\pi )/(36\pi )` =
`(x)/(360)`, that is

`(1)/(9)` =
`(x)/(360)` ( cross- multiply )

9x = 360 ( divide both sides by 9 )

x = 40

Hence central angle = 40°