Constructing a 20-Degree Angle with Ruler and Compass: A Step-by-Step Guide

Constructing a 20-degree angle using only a ruler and compass can seem challenging at first, but with a few precise steps, it becomes a manageable task. This article will walk you through the process, providing a detailed guide to help you achieve accuracy. Let's dive into the construction method.

Steps to Construct a 20-Degree Angle

1. Draw a Base Line

Start by using your ruler to draw a horizontal line segment AB. This line will serve as the base for the angle you want to construct.

2. Construct a 60-Degree Angle

To create a 60-degree angle, follow these steps:

Place the compass point on point A and draw an arc that crosses the line AB at point C and extends above the line. Without changing the compass width, place the compass point on point C and draw an arc above the line. Now, keeping the compass width constant, place the compass point on point A again and draw another arc that intersects the previous arc. Label the intersection point as D. Draw a line from point A through point D. This line AD creates a 60-degree angle with line AB.

3. Bisect the 60-Degree Angle

To find the 30-degree angle, you need to bisect the 60-degree angle CAD.

With the compass point on point C, draw an arc that crosses both lines AC and AD. Label the intersection points as E and F. Without changing the compass width, place the compass point on point E and draw a small arc. Do the same from point F to create another arc that intersects the first arc. Label the intersection point as G. Draw a line from point A through point G. This line AG creates a 30-degree angle with line AB.

4. Bisect the 30-Degree Angle

To find the 15-degree angle, bisect the 30-degree angle CAG using the same method as before.

Draw arcs from points C and G to find intersection points H and I above line AB. Draw an arc from point H and another from point I to find their intersection point J. Draw a line from point A through point J. This line AJ creates a 15-degree angle with line AB.

5. Combine to Get 20 Degrees

Now, to construct a 20-degree angle, combine the 30-degree angle AG and the 15-degree angle AJ.

Draw an arc from point A to point G to create a 30-degree angle and then from point G to point J to create a 15-degree angle. The angle AGJ is the desired 20-degree angle.

Summary

By combining angles and using the method of bisecting angles, you can construct a 20-degree angle accurately using just a ruler and a compass. This method relies on first creating known angles (60 degrees), then bisecting to obtain 30 degrees and 15 degrees, and carefully combining them to achieve the desired angle. Practice these steps to master the technique and create precise 20-degree angles.