

Supplementary angle
Geometry construction using a compass and straightedge
This construction takes a given angle and constructs its
supplementary angle.
Recall that the supplementary angle is one that makes the given angle become 180°.
So an angle of 45° has a supplementary angle of 180°  45° = 135°.
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∠DAB + m∠BAC = 180° 
A linear pair, so add to 180° 
2 
∠DAB is the supplementary angle to ∠BAC 
From (1) 
 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
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Right triangles
Triangle Centers
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NonEuclidean constructions
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