We can find the lengths of arcs when we know their measure and the radius because the measure indicates the fraction of the circumference we need to include.
Here we have circle with circumference [tex]C=2\pi r = 10 \pi \textrm{ inches}[/tex]
122 degrees is a fraction of that circumference, so has length
[tex] d = \dfrac{122^\circ}{360^\circ} 10 \pi } = 10.6465... [/tex]
Answer: 10.65
