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madreJ [45]
3 years ago
10

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 ang

le
Mathematics
1 answer:
Fiesta28 [93]3 years ago
7 0

Answer:

114.59\°

Step-by-step 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

\frac{360}{6\pi } \frac{degrees}{cm} =\frac{x}{6} \frac{degrees}{cm} \\ \\x=6*360/(6\pi )\\\\ x=114.59\°

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