

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 stepbystep instructions
The above animation is available as a
printable stepbystep 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
NonEuclidean constructions
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