Constructing a 60° angle
This shows how to construct a 60° angle from scratch using a compass and straightedge. If you already have one of the angle sides given, you can skip the first step. This process is very similar to part of the construction of an equilateral triangle, which has all internal angles 60°

By constructing a 60° angle and then bisecting it you can make a 30° angle. See Bisecting an angle with compass and straightedge

Also see:
Constructing a 45° angle
Constructing a 30° angle

Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)

Step-by-step Instructions
Step 1 Draw a line segment which will become one side of the angle. (Skip this step if you are given this line.) The exact length is not important. Label it PQ. P will be the angle's vertex.
Step 2 Set the compass on P, and set its width to any convenient setting.
Step 3 Draw an arc across PQ and up over above the point P.
Step 4 Without changing the compass width, move the compass to the point where the arc crosses PQ, and make an arc that crosses the first one.
Step 5 Draw a line from P, through the intersection of the two arcs.
Step 6 Done. The angle QPR has a measure of 60°
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

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions