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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.
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Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions