Answer:
∠DFE = 56°
Explanation:
You want the measure of the inscribed angle DFE marked (x-1°) that intercepts the same arc as the central angle marked (x+55°).
Intercepted arc
An inscribed angle is half the measure of the arc it intercepts. A central angle has the same measure as the arc it intercepts. This tells us ...
∠DFE = 1/2·∠DGE
2·∠DFE = ∠DGE . . . . . . multiply by 2
∠DFE = ∠DGE -∠DFE . . . . . subtract ∠DFE
∠DFE = (x +55°) -(x -1°) . . . . . substitute marked values
∠DFE = 56° . . . . . . . . . . . . . . . simplify
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Additional comment
We could have solved for x and used that to find ∠DFE. Since x has a coefficient of 1 in both angle expressions, we can get directly to the answer by looking at the difference of the angles. When one angle is 2 times the other, their difference is equal to the smaller angle, which is the one we wanted. It isn't always necessary to solve for x. (x=57° in case you're wondering.)