

Sum of angles
Geometry construction using a compass and straightedge
This construction takes one given angle and copies it adjacent to another, creating a larger angle whose measure is the sum of the two.
By carrying out this construction more than once, any number of angles can be summed.
This can be done by adding each successive angle to the left or the right of the accumulating angle.
In a similar way, angles can be 'subtracted'. See the construction:
Difference of two angles.
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.
Proof

Argument 
Reason 
1 
Angle ∠BAC is congruent to angle ∠SPR 
Copied using the procedure described in
Copying an angle. See that page for proof. 
2 
m∠SPQ = m∠SPR + m∠RPQ 
Adjacent angles. 
3 
m∠SPQ = m∠BAC + m∠RPQ 
From (1), (2) 
 Q.E.D
Try it yourself
Click here for a printable worksheet containing two angle copying 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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