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.
To construct the equilateral triangle, we:
Connect the tip of the triangle to one end of the base, and you will have a 60° angle.
To construct a 30° angle, you must first construct a 60° angle as above and then bisect the angle.
To construct a 90° angle, you draw a base line and then construct a perpendicular bisector to leave a 90° 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.