Constructing an angle

Constructing a 60° angle

To construct a 60° angle, we first draw a line of any length. Then using a compass, we use this as a base to construct an equilateral triangle.

Two lines forming angle RPQ which is labelled 60°. There is an arc at point R.

To construct the equilateral triangle, we:

  • open the compass to the same dimensions as our original line
  • place the point of the compass on one end of the line and draw an arc
  • repeat this at the other end and the arcs should intersect where the tip of the triangle should be

Connect the tip of the triangle to one end of the base, and you will have a 60° angle.

Constructing a 30° angle

To construct a 30° angle, you must first construct a 60° angle as above and then bisect the angle.

Angle RPQ bisected to form two angles labelled 30°

Constructing a 90° angle

To construct a 90° angle, you draw a base line and then construct a perpendicular bisector to leave a 90° angle.

A 90° angle formed by a base line and a perpendicular bisector

Constructing a 45° angle

To construct a 45° angle, first construct a perpendicular bisector of a line to leave a 90° angle. Secondly, following the steps above, bisect the angle. This should leave you with a 45° angle.

A 90° angle bisected to to form two angles labelled 45°