A central angle in a circle with a radius of 3 cm intercepts an arc with a length of 6 cm what is the measure of the central angle

Question

asked May 3, 2020 156k views

1 Answer

Santiago Munez · Answer 1 · 2020-05-09T04:05:19+0000

Answer:

$114.59\°$

Explanation:

we know that

The circumference of a circle is equal to

$C=2\pi r$

In this problem we have

$r=3\ cm$

substitute

$C=2\pi (3)=6 \pi\ cm$

Remember that

$360\°$ subtends the arc length of the complete circle

so

by proportion

Find the measure of the central angle for an arc length of
$6\ cm$

$(360)/(6\pi ) (degrees)/(cm) =(x)/(6) (degrees)/(cm) \\ \\x=6*360/(6\pi )\\\\ x=114.59\°$