A single-component droplet placed on a completely wetting substrate shows a pseudostable apparent contact angle (θapp) during evaporation. We propose a simple theory to explain the phenomenon accounting for the liquid evaporation and the internal flow induced by the capillary and Marangoni effects. The theory predicts that when evaporation starts, the contact angle approaches to θapp in a short time τs, remains constant for most of the time of evaporation, and finally increases rapidly when the droplet size becomes very small. This explains the behavior observed for alkane droplets. Analytical expressions are given for the apparent contact angle θapp and the relaxation time τs, which predict how they change when the evaporation rate, droplet size, and other experimental parameters such as thermal conductivity of the substrate are changed.