

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 stepbystep instructions
The above animation is available as a
printable stepbystep 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.
Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
(C) 2009 Copyright Math Open Reference. All rights reserved

