The concept of angles is important for future geometric knowledge (Arslan et al., 2016; Moore, 2013; Yigit, 2014). However, although Piaget (1948) suggests angles lead to the discovery of lines, angles are typically taught later in schools, after points, lines, and planes (Charles, 2011). Therefore, the way in which angles are taught can affect how students conceptualize angles. This study investigates such phenomena by using APOS theory and a preliminary genetic decomposition. Data was collected from a fifth grade student, a seventh grade student, and a twelfth grade student. Results show: the fifth grader developed a 2- and 1-line schema for angles; the seventh grader developed a 2-line schema; and the twelfth grader developed a 2-, 1-, and 0-line schema. Overall, the students contradicted the genetic decomposition model due to the fluidity of their thinking. This study provides teaching implications as well as areas for future research.