Find the measures of all of the angles in the parallelogram.

In a parallelogram, the opposite angles are equal so:
FED = DGF = 59x - 1
EDG = GFE = 121x + 1
And now since we know angles in a quadrilateral always add up to 360°, we can create an equation and solve for x:
2(59x - 1) + 2(121x + 1) = 360
118x - 2 + 242x + 2 = 360
360x = 360
x = 1
Now sub into our angle equations:
FED = DGF = 59(1) - 1 = 58°
EDG = GFE = 121(1) + 1 = 122°