Constructing a 20 Degree Angle using Ruler and Compass

Ahoy there readers! This can be labelled as the first 'constructive' post of my blog. Yes Indeed, it is literally "CONSTRUCTIVE".

I will be showing you an extremely simple method to Draw a 20-Degree Angle using Ruler and Compass only in 4 steps. This method is my own, and I came across it sometime in 6th grade when I 'misconstructed' a 30-degree angle. Till now, after hours of searching, I have yet not found a proper method of constructing a 20-degree angle with ruler and compass on the internet. Before revealing the method, I will try to give an introduction to Compass and Straightedge construction. Before beginning, let me make it clear that I am no mathematician, and you are free to criticize any aspect of this post.

Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angle, and other geometric figures using only a ruler and compass. This was the classical Greek way of Geometry. But the Greeks did not find constructions for three problems, one of them being Angle Trisection. Angle Trisection is still considered impossible, and so is constructing a 20 degree angle with compass and straightedge.

Angles that can be constructed by Compass and Straightedge are 15,30,45,60,90,120,150,180 degrees and some other angles can be constructed by Bisection (for eg. 7.5 degrees, 22.5 degrees e.t.c). Constructing a 20 degree angle can help you in constructing 10,40,50,70,80,100,110,130,140,160,170 degree angles with only a Ruler and Compass (and your pencil)!

Given below is my method of carrying out the construction of a 20 degree angle using a straightedge and compass. It is very accurate and you get a perfect measure everytime! Readers, feel free to criticize, point out mistakes and also, don't forget to Praise! And hey, also make an effort to see if this construction had been carried out before (and comment below, please)!

The figures below are my own work, and are not perfect drawings, and the image is only a representation, not an actual geometric construction.

CONSTRUCTING A 20 DEGREE ANGLE USING COMPASS AND STRAIGHTEDGE (RULER) ONLY

1. Step 1:

- Draw a line segment PQ. With centre O, Draw an arc of any length using your compass an

d label it as AB.

2. Step 2:

- Keeping your compass wide open with the same length, draw an arc S on AB. This will be your normal 60 Degree angle arc. (If you join S to O, you will get an angle measuring 60 degrees i.e. Angle SOB).

3. Step 3:

- Bisect the 60 degree angle and name the point of intersection as J. J will be your normal 30 degree arc. (After bisecting the 60 degree angle, if you join J to O you will get an angle measuring 30 degrees i.e. Angle JOB).

Till Step 3, it was a normal construction. Step 4 is where the 'Twist' occurs!!!

4. Step 4:

- Join the arc J to A, and there you have it! Angle JAB is your 20 degree angle! Now you can easily construct angles measuring 10,40,50,70,80,100,110,130,140,160,170 degrees!

PS. If you still didn't understand the construction, or have any queries, mail me at atharvjoshi@ymail.com.

Later!