Question

What is the measure of the corresponding central angle for XY in radians?

Answer 1

A

Explanation:

the length of arc XY is calculated as

arc = circumference of circle × fraction of circle

= 2πr ×
`(0)/(2\pi )` ( r is radius and Θ is central angle )

here arc = 40 and r = 10 , then

2π × 10 ×
`(0)/(2\pi )` = 40

20π ×
`(0)/(2\pi )` = 40 ( cancel 20π and 2π by 2π )

10Θ = 40 ( divide both sides by 10 )

Θ = 4 radians

Answer 2

4 radians

Explanation:

Arc Length (Radians) = rθ

Given Arc Length XY = 40cm and radius, r = 10cm,

we will substitute these 2 values into the formula to find θ.

(10)θ = 40

θ = 40 / 10

= 4 radians