General Certificate of Secondary Education (GCSE) Maths Practice Exam

The construction of a 60-degree angle using a compass is effectively achieved by utilizing the intersections of arcs. To illustrate this method, one begins by drawing a circle with a compass from a point, which serves as the vertex of the angle. This circle will intersect the baseline at two distinct points.

Next, keeping the compass width the same, one draws arcs above and below the line from both points where the circle intersects the baseline; these arcs will cross at two points. Connecting the vertex to this intersection creates two angles, and through this geometric process, one of those angles will be precisely 60 degrees, forming an equilateral triangle with equal lengths on all sides due to the inherent properties of circles and triangles.

This method reliably and accurately allows for the construction of a 60-degree angle without requiring direct measurement, demonstrating symmetry and the fundamental principles of geometric constructions. The precision of intersection points is key in achieving a perfect angle, illustrating why this technique stands out for constructing a 60-degree angle.