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Complementary angle
Geometry construction using a compass and straightedge

This construction takes a given angle and constructs its complementary angle. Recall that the complementary angle is one that makes the given angle become 90°. So an angle of 30° has a supplementary angle of 90° - 30° = 60°.

In this construction you can extend either leg back. It will produce the same result.

Proof

This is the same drawing as the last step in the above animation.

  Argument Reason
1 m∠FAC = 90° Drawn at point A using the construction Perpendicular to a line at a point. See that page for proof.
2 m∠FAB + m∠BAC = ∠FAC Adjacent angles
2 m∠FAB and m∠BAC are complementary m∠FAB + m∠BAC = 90° See (2)

  - Q.E.D

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.

Try it yourself

Click here for a printable worksheet containing two supplementary angle angle problems. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions