This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in Turkey. Qualitative and quantitative research methods were used for data collection and analysis. 4 questions about the concepts of degree and radian were asked to the prospective mathematics teachers. The responses of the prospective teachers were categorized as correct and incorrect. Then, incorrect answers were divided into sub-categories by means of coding method and presented in tables. According to research findings, 40% of the prospective mathematics teachers defined the concept of degree correctly while approximately 90% made an incorrect definition of radian.