Answer:
216 degrees
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference of the circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=10\ in[/tex]
substitute
[tex]C=2\pi (10)[/tex]
[tex]C=20\pi\ in[/tex]
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
[tex]\frac{360}{20\pi}=\frac{x}{12\pi}\\ \\x=360*12/20\\ \\x= 216\°[/tex]
