What is the method to construct a 60-degree angle?

To construct a 60-degree angle, use a compass and straightedge to create an equilateral triangle.

First, draw a straight line segment, which will be one side of the equilateral triangle. Label the endpoints of this segment as points A and B. Place the compass point on A and draw an arc above the line segment. Without changing the compass width, place the compass point on B and draw another arc that intersects the first arc. Label the intersection point of the arcs as point C.

Next, use the straightedge to draw line segments AC and BC. Since all sides of an equilateral triangle are equal, each angle in the triangle will be 60 degrees. Therefore, the angle ∠CAB is 60 degrees.

This method works because an equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees. By constructing such a triangle, you ensure that the angle you create is precisely 60 degrees. This technique is fundamental in geometry and is often used as a building block for more complex constructions.