The receding contact angles of water drops on PMMA and PET surfaces were determined by using video microscopy to follow the time-dependent evaporation of sessile drops. Depending on the initial drop size, receding angles of theta(r) = 54-64 degrees for PMMA and theta(r) = 64-66 degrees for PET were found with an average hysteresis of 23.5 +/- 1.5 and 19.5 +/-1.5 degrees, respectively. Advancing and receding angles, theta(a) and theta(r), were also determined by the needle-syringe and the inclined plane methods for comparison. The discrepancies from the mean of the maximum and minimum contact angle results of both the needle-syringe and the inclined plane methods were larger than expected for all the polymer surfaces. A general trend was seen with samples giving a larger hysteresis also producing a larger discrepancy for all the samples. The major cause of this discrepancy is the variation of the rate of liquid introduction and withdrawal with the syringe in the needle-syringe method and the drop size effect in the inclined plane method. In this respect the drop evaporation method allows a rate of liquid withdrawal which minimizes (or standardizes) the linear rate of retreat effect on receding contact angle measurement. The literature values are also given for comparison. A discrepancy of 11-15% from the mean for theta(a) and 27-32% for theta(r) is reported in the literature for these polymers. This is approximately five times more than the previously claimed 2-3% deviation from the mean for theta(a) on the same clean homopolymer samples.