This study investigates the identification and extraction of the shock-wave angle over a conical model in a supersonic wind tunnel using images acquired by an optical Schlieren system. The proposed method consists of noise reduction using a bilateral filter, edge detection using the Canny algorithm, point clustering using DBSCAN, and geometric fitting to automatically extract the dominant shock-wave structure and determine its angle. The method was applied to flow images obtained at a Mach number of 3 and a cone angle of 20°. The measured shock-wave angle was 29.20°. Comparison with the reference value of 29.65° yielded a deviation of 0.45°. Furthermore, application of the method to two images resulted in a standard deviation of 0.5°, indicating satisfactory repeatability. The angular measurement uncertainty was estimated to be 0.6°. The results demonstrate that the proposed method can identify and measure shock-wave geometry with satisfactory repeatability and minimal operator intervention. In this study, the method was validated for approximately linear shock waves under the investigated conditions; direct extraction of other flow-field parameters was beyond the scope of the research.