Question

If a circle has a radius of 16, and an arc length of 12, what is the angle measure of the central angle that matches that arc?

Answer 1

135°

Explanation:

The arc length is calculated as

EF = circumference of circle × fraction of circle

= 2πr ×
`(?)/(360)`

Given EF = 12π , then

2π × 16 ×
`(?)/(360)` = 12π ( divide both sides by 2π )

16 ×
`(?)/(360)` = 6 ( multiply both sides by 360 to clear the fraction )

16 ? = 2160 ( divide both sides by 16 )

? = 135°