When there are connected gears, the arc lenght must be equal. That is:
When the smaller gear has completed one full rotation, we have

since R=7in and r=4 in, we have that

and we must isolate theta_1. Hence, the answer in radians is

Now, we must convert radians to degrees. This can be given by applyng the rule of three:

therefore, x is equal to

hence, in degrees the answer is 205.71 degrees