How to make a 120 degree angle without a protractor

Updated February 21, 2017

Being able to draw angles without the aid of a protractor is an important architectural and mathematical skill. Many angles can be drawn with a compass, also known as a pair of compasses. A compass is a drawing tool with two pivoting legs, one ending in a spike and the other ending in a pencil point. The ratio of the circumference of a circle to its diameter is very close to 3:1, and because 120 degrees is a third of a full circle, a pair of compasses can be used to draw a 120-degree angle.

Mark a dot on a sheet of paper. Draw a circle using a compass and a sharp pencil, using the dot as the centre point. Take care not to alter the compass setting when the circle is complete.

Place a ruler over the circle with the edge passing through the centre of the circle and any point on the perimeter of the circle. Make a clear mark where the ruler crosses the circumference.

Ensure that the radius of the compass has not changed, and then place the pivot point on the mark where the straight line crossed the circle perimeter. Draw a new circle.

Draw straight lines from the centre of the first circle to the two points where the second circle crosses the perimeter of the first circle. This creates the points of two equilateral triangles, with internal angles of 60 degrees. The angle between these two lines is 120 degrees.


Many different angles can be drawn using a compass and a ruler, including those measuring 30, 45, 60, 90 and 180 degrees.


The radius of the compass must remain unchanged throughout the process. If it changes, reset it to the original value.

Things You'll Need

  • Drawing compass
  • Ruler
  • Sharp pencil
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About the Author

David Robinson has written professionally since 2000. He is a Fellow of the Royal Geographical Society and the Royal Meteorological Society. He has written for the "Telegraph" and "Guardian" newspapers in the U.K., government publications, websites, magazines and school textbooks. He holds an honors Bachelor of Arts in geography and education and a teaching certificate from Durham University, England.