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The area of the shaded region can be gotten by multiplying the area of the circle by the subtended angle of the sector.
45
It is found by: (sector area/entire circle area) times 360 in degrees
Well, darling, if you shaded all but three eighths of the rectangle, then the shaded area is 5/8 of the total rectangle. To find the percentage of the rectangle that is not shaded, you subtract the shaded area from 100%. So, 100% - 62.5% (5/8 as a percentage) = 37.5%. Voilà, 37.5% of the rectangle is not shaded.
You cannot. The angle of the sector MUST be given, although that might be implicitly rather than explicitly.