How to construct a 30 degree angle with compass and straightedge or ruler

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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 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 a rhombus. Its two diagonals form four 30-60-90 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 PS, and angle PAS is a right angle	Diagonals of a rhombus bisect each other at right angles. See Rhombus definition.
4	Triangle ∆PAS is a 30-60-90 triangle.	∆PAS is a right triangle with two sides in the ratio 1:2. (third side would be √3 by pythagoras).
5	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.

Printable step-by-step instructions

Proof

Try it yourself

Constructions pages on this site

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Angles

Triangles

Triangle Centers

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Non-Euclidean constructions