Angles on One Side of a Line: Completing the Straight Angle

This example demonstrates how to determine a missing angle created by several rays lying on one side of a reference line, where the overall configuration corresponds to a straight angle (a 180° angle). The central ideas are the structure of a straight angle formed by opposite rays, angle-partition relationships, and solving for an unknown angle using geometric constraints (angle sums). Construction-wise, the figure is built by defining a base line and key points, creating rays from those points, and labeling the variable angles (α, β, γ, δ, etc.), after which the missing angle is obtained from the imposed angle relations. In the GeoGebra setup, the main commands and geometric elements include Line, Point, Ray, Angle, Segment, Polygon, Vector, and Translate; the construction uses labeled points such as A, B, C, D, E, F and angle variables such as α, β, γ, δ, along with translated/related objects (e.g., primed points like G′, H′, I′, J′) to express positional dependencies. Suitable for secondary-school geometry lessons, angle-chasing practice, and contest-style reasoning.