Question

Central angle measure

Answer 1

Answer:

40°

Step-by-step explanation:

In any circle the following ratios are equal

let x be the measure of the central angle, then

$\frac{arc}{circumference}$ = $\frac{x}{360}$

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

$\frac{4\pi }{36\pi }$ = $\frac{x}{360}$, that is

$\frac{1}{9}$ = $\frac{x}{360}$ ( cross- multiply )

9x = 360 ( divide both sides by 9 )

x = 40

Hence central angle = 40°