The COVID-19 pandemic has forced governments around the globe to apply various preventive measures for public health. One of the most effective measures is wearing face masks, which plays a vital role in blocking the transmission of droplets and aerosols. To understand the protective mechanism of face masks, especially in indoor environments, we apply a computational fluid dynamics technique to predict the lifetime of cough droplets. Therefore, we can assess the exposure risk in a ventilated room where an infected individual wears a face mask or not. We focus on the dynamic evaporation and diffusion of droplets in a human-cough process, which is a major cause for the spread of the virus. We find that wearing a face mask can effectively reduce the total mass and Sauter mean diameter of the residual droplets after a single cough. The mass concentration of virus-carrying droplets in the ventilated room decreases by 201, 43,786, and 307,060 times, corresponding to wearing cotton face masks, surgical face masks, and N95 face masks, respectively. However, the maximum travel distance of 80% droplets is insensitive to wearing a face mask or not. Therefore, the residual droplets are widely distributed due to the influence of indoor airflow. Furthermore, we study aerosol exposure risks in different areas of the room and find that high concentrations of aerosols occur in the streamline through an infected individual, especially next to the individual within 1.5 m. This strongly suggests a social distance despite the fact that the majority of droplets are filtered by face masks. This study explains the impact of face masks and airflow on indoor exposure risks and further inspires potential measures for public health, for example, no individuals should sit near the air supply opening.