Objectives This study aimed to examine the relationships between daily stress factors (parents, economy, grades, school, peers, and appearance) perceived by adolescents and verify the mediating effect of anger coping styles in the relationship between daily stress factors and happiness. Methods The participants were 468 adolescents attending middle and high schools in the Gwangju and Jeonnam regions. This study conducted frequency analysis, reliability test, and correlation analysis using the SPSS WIN 23.0 program and examined the mediating effect using Process Macro Model 4. Results The findings revealed that daily stress factors (parents, grades, school, peers, appearance, and economy) affected adolescents’ happiness. Secondly, parental, academic, school, and economy-related stress influenced anger coping styles. Thirdly, anger coping styles mediated the relationship between daily stress and happiness. Specifically, economic stress showed a full mediating effect, while parentak, academic, and school-related stress had a partial mediating effect. However, peer and appearance-related stress had no mediating effect. Conclusions These results confirm that daily stress factors influence both happiness and anger coping styles among adolescents, with economic, parental, academic, and school-related stress factors showing mediating effects. Thus, this study emphasized the importance of addressing and intervening in stress factors affecting adolescents and discussed suggestions for future studies.