One challenging aspect of the Connected and Automated Vehicle (CAV) operation in mixed traffic is the development of a situation-awareness module for CAVs. While operating on public roads, CAVs need to assess their surroundings, especially the intentions of non-CAVs. Generally, CAVs demonstrate a defensive driving behavior, and CAVs expect other non-autonomous entities on the road will follow the traffic rules or common driving behavior. However, the presence of aggressive human drivers in the surrounding environment, who may not follow traffic rules and behave abruptly, can lead to serious safety consequences. In this paper, we have addressed the CAV and non-CAV interaction by evaluating a situation-awareness module for left-turning CAV operations in an urban area. Existing literature does not consider the intent of the following vehicle for a CAVs left-turning movement, and existing CAV controllers do not assess the following non-CAVs intents. Based on our simulation study, the situation-aware CAV controller module reduces up to 27% of the abrupt braking of the following non-CAVs for scenarios with different opposing through movement compared to the base scenario with the autonomous vehicle, without considering the following vehicles intent. The analysis shows that the average travel time reductions for the opposite through traffic volumes of 600, 800, and 1000 vehicle/hour/lane are 58%, 52%, and 62%, respectively, for the aggressive human driver following the CAV if the following vehicles intent is considered by a CAV in making a left turn at an intersection.