Final answer:
You can bisect an angle using only a straightedge and compass by creating intersecting arcs and drawing a line from their intersection point to the original angle's vertex. This procedure is a standard technique in geometry.
Step-by-step explanation:
It is possible to bisect an angle using only a straightedge and compass. The process is a fundamental construction in geometry and involves a sequence of steps that create two equal angles from a single angle. Firstly, one must use the compass to draw an arc that crosses both rays of the angle. Secondly, using the points where the arc crosses the rays, draw two more arcs that intersect above the angle. Lastly, join the intersection point of these two arcs to the vertex of the angle with a straight line using your straightedge. This resulting line bisects the original angle into two equal angles.
Here are the steps to bisect an angle:
1.Draw a ray (line) with the given angle vertex as its endpoint.
2.Place the compass at the vertex and draw two arcs intersecting the rays of the angle to create two points (Label them A and B).
3.With the same radius, place the compass at point A and draw an arc above and below the original angle.
4.Do the same with the center at point B.
5.Draw a straight line connecting the intersections of the arcs above the original angle to the intersections of the arcs below the original angle.
6.The resulting line will bisect the original angle into two equal parts.