Question

If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc? 216 degrees 270 degrees 288 degrees

Answer 1

216 degrees

Explanation:

step 1

Find the circumference of the circle

The circumference of the circle is equal to

`C=2\pi r`

we have

`r=10\ in`

substitute

`C=2\pi (10)`

`C=20\pi\ in`

step 2

Find the measure of the arc if the length of the arc is 12π in

Remember that

The circumference of a circle subtends a central angle of 360 degrees

so

by proportion

`(360)/(20\pi)=(x)/(12\pi)\\ \\x=360*12/20\\ \\x= 216\°`