Answer
$213^\circ$
Work Step by Step
1. We know that the two gears should travel the same arc length.
2. For the smaller gear, we have the arc length traveled as $L_1=4.8\times315^\circ\times\frac{\pi}{180^\circ}\ in$
3. For the larger gear, we have the arc length traveled as $L_2=7.1\times \theta^\circ\times\frac{\pi}{180^\circ}\ in$
4. Let $L_2=L1$, we can find $\theta=\frac{4.8\times315}{7.1}\approx213^\circ$
