If one folds a thin viscoelastic sheet under an applied force, a line of plastic deformation is formed which shapes the sheet into an angle. We determine the parameters that define this angle experimentally and show that, no matter how much load one applies, it is impossible to make angles less than a certain minimum angle in a definite time. Moreover, it is shown that regardless of whether the sheet is released freely afterward or kept under the load, a logarithmic relaxation process follows the first deformation. The slope of this logarithm is the same in both conditions and depends neither on the applied force nor on the thickness of the sheet, which indicates it is directly a probe of the molecular mobility of the material. This intrinsic relaxation constant was measured 0.01 and 5.7 for Mylar and paper sheets, respectively. It is also suggested that the observed minimum angle of folding can be defined as a characteristic index for the plasticity of different materials.