
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.
Constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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