Constructing a 60° angle
Geometry construction using a compass and straightedge

This page shows how to construct (draw) a 60 degree angle with compass and straightedge or ruler. This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. We use one of those angles to get the desired 60 degree result. See the proof below for more details.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

Proof

This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. The image below is the final drawing above with the red items added.

  Argument Reason
1 Line segments AB, PB, PA are congruent All drawn with the same compass width.
2 Triangle APB is an equilateral triangle Equilateral triangles are those with all three sides the same length.
3 Angle APB has a measure of 60° All three interior angles of an equilateral triangle have a measure of 60°. See Equilateral triangle definition

  - Q.E.D

Try it yourself

Click here for a printable worksheet containing two 60° angle exercises. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Tangents

Ellipses

Polygons

Non-Euclidean constructions

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