Which method is used to construct a 60-degree angle?

The method of constructing a 60-degree angle using a compass is based on the geometric principle that a regular hexagon can be inscribed in a circle, and each central angle of the hexagon measures 60 degrees.

To do this, you start by drawing a circle with a compass, which will act as the boundary for your angle. Mark the center of the circle as point O. From the center, you then draw a radius to any point on the circle, and label that point as A. Without changing the width of the compass, place the compass point on A, and draw another arc that intersects the circle at point B. Next, keeping the compass width the same, place the compass point on B and draw an arc intersecting the radius. Where this new arc intersects the radius, label that point C.

Finally, drawing a straight line from O to C creates a 60-degree angle with the original radius OA. This method is accurate and does not rely on measurement tools, as it purely uses the properties of circles and angles to construct the desired angle.

Using a protractor to measure directly would provide a quick way to create a 60-degree angle but does not utilize geometric constructions. Drawing two intersecting lines could