An arc of \( \Large 60 ^{\circ} \) in one circle is double the arc in a second circle whose radius is three times that of the first circle. What is the degree measure of the arc of the second circle?

Length of arc, \( \Large l=\frac{2 \pi r \times 60 ^{\circ} }{360 ^{\circ} }=\frac{2 \pi r}{6}=\frac{ \pi r}{3} \)

Now, \( \Large \frac{l}{2} = \frac{2 \pi r \theta }{360 ^{\circ} } \)

=> \( \Large \frac{ \pi r}{6} = \frac{2 \pi r \theta }{360 ^{\circ} } \)

=> \( \Large \theta = 30 ^{\circ} \)