

Constructing a 30° angle
Geometry construction using a compass and straightedge
This page shows how to construct (draw) a 30 degree angle with compass and straightedge or ruler. It works by first creating a
rhombus
and then a
diagonal of that rhombus.
Using the properties of a rhombus it can be shown that the angle created has a measure of 30 degrees. See the proof below for more on this.
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 a rhombus.
Its two diagonals form four 306090 triangles.
The image below is the final drawing above with the red items added.

Argument 
Reason 
1 
Line segments PT, TR, RS, PS, TS are congruent (5 red lines) 
All created with the same compass width. 
2 
PTRS is a rhombus. 
A rhombus is a quadrilateral with four congruent sides. 
3 
Line segment AS is half the length of TS, and angle PAS is a right angle 
Diagonals of a rhombus
bisect each other at right angles. See Rhombus definition. 
4 
Line segment AS is half the length of PS 
PS is congruent to TS. See (1), (3) 
5 
Triangle ∆PAS is a 306090 triangle. 
∆PAS is a right triangle with two sides in the ratio 1:2. (third side would be √3 by pythagoras). 
6 
Angle APS has a measure of 30°. 
In any triangle, smallest angle is opposite shortest side. 
 Q.E.D
Try it yourself
Click here for a printable worksheet containing two 30° 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
NonEuclidean constructions
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