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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 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.

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

Non-Euclidean constructions