Question

If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc?

A.
60°
B.
90°
C.
120°
D.
180°

Answer 1

A

Explanation:

The arc length formula is:

Arc Length =
`(\theta)/(360)*2\pi r`

Where

`\theta` is the angle measure of the arc, and

2πr is the circumference

Putting 84 in place of circumference and 14 in place of arc length, we can solve for
`\theta`:

Arc Length =
`(\theta)/(360)*2\pi r`

14 =
`(\theta)/(360)*(84)`

14 =
`(84\theta)/(360)`

`14*360=84\theta\\5040=84\theta\\\theta=(5040)/(84)=60`

answer choice A is right.