On other pages there are instructions for constructing angles of 30°, 45°, 60° and 90°. By combining them you can construct other angles.

For example, by first constructing a 30° angle and then a 45° angle, you will get a 75° angle. The table below shows angles that can be obtained by combining simpler ones in various ways:

Furthermore, by combining three angles many more can be constructed.

You can subtract them too

By constructing an angle "inside" another you can effectively subtract them. So if you started with a 70° angle and constructed a 45° angle inside it sharing a side, the result would be a 25° angle.

The basic constructions are described on these pages:

• Constructing a 30° angle
• Constructing a 45° angle
• Constructing a 60° angle
• Constructing a 90° angle

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy method)
• Parallel line through a point (rhombus method)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object