Answer:
[tex]114.59\°[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
In this problem we have
[tex]r=3\ cm[/tex]
substitute
[tex]C=2\pi (3)=6 \pi\ cm[/tex]
Remember that
[tex]360\°[/tex] subtends the arc length of the complete circle
so
by proportion
Find the measure of the central angle for an arc length of [tex]6\ cm[/tex]
[tex]\frac{360}{6\pi } \frac{degrees}{cm} =\frac{x}{6} \frac{degrees}{cm} \\ \\x=6*360/(6\pi )\\\\ x=114.59\°[/tex]
