DOI: https://doi.org/10.36347/sjpms.2026.v13i07.001

Pages: 241-249

The term "Angle Multi-section" refers to the process of dividing an angle into n equal sub-angles, n ∈ N, using only a straightedge and compass within the framework of Euclidean geometry. This problem is derived from the previously published article, "An Exact and Simple Solution to the ‘Trisecting An Angle’ Problem Using Straightedge and Compass," and "An Exact and Simple Solution to the ‘Quinti-secting An Angle’ Problem Using Straightedge and Compass" [8, 9, 18]. In ancient Greek mathematics, three classical problems significantly influenced the development of geometry: Squaring The Circle, Trisecting an Angle, and Doubling the Cube. Similarly to Trisecting an Angle problem, the multi-section of a given angle is just a generalisation problem in Euclidean Geometry. The problem of angle multi-section specifically involves constructing an angle that is exactly one-n^th of a given arbitrary angle using only an unmarked straightedge and a compass. This thesis concentrates solely on the multi-sectioning process for arbitrary angles. I present 2 classical straightedge-and-compass constructions that achieve exact trisection & penta-section/quinti-section while avoiding the explicit use of π. This approach employs a ruler-based geometric analysis and synthesis. Although trisection for specific angles (such as a right angle, equilateral triangle angle. …) is relatively a feeling idea straightforward, addressing the general case has not been explored within classical constraints. The concept of angle quinti-section/penta-section was formulated in December 2025, as a continuation of my research on the Angle Trisection, which was solved precisely and simply and subsequently published in SJPMS [8, 9]. The results of this research provide an exact construction-based solution to the challenge of angle multi-section process of an angle utilizing only a straightedge and compass in Euclidean geometry. While the solution relies on theorems and corollaries from secondary geometry, it