What is a crucial part of the process to bisect an angle?

To bisect an angle, drawing arcs from the vertex is a crucial step. When you begin the bisecting process with a compass, placing the point of the compass at the vertex of the angle allows you to draw arcs that intersect the two lines forming the angle. This creates two intersection points on each ray of the angle that are equidistant from the vertex.

The next step involves using a straightedge to draw a line from the vertex through the point where the two arcs intersect. This results in two equal angles, effectively bisecting the original angle. The reason drawing arcs is vital is that it establishes a geometrically precise method for finding the midpoint of the angle without needing measurements or tools like a protractor.

While drawing a straight line from the vertex and using a protractor may be applicable in some contexts, they do not directly contribute to the actual bisection process. Similarly, measuring each angle is not necessary when the goal is to create two equal angles through construction rather than measurement.