What is the procedure to construct an angle of 120 degrees?

To construct a 120-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 A and B. Place the compass point on A and draw an arc above the line. 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 C.

Next, use the straightedge to draw line segments AC and BC. Since all sides of an equilateral triangle are equal, each internal angle of the triangle is 60 degrees. To get a 120-degree angle, extend one of the sides of the triangle. For example, extend the line segment AB beyond B. The angle formed between the extended line and the line segment BC will be 120 degrees because it is the external angle of the equilateral triangle.

This method ensures accuracy and uses basic geometric tools, making it ideal for GCSE Maths students.