How to Copy an Angle Using a Compass

By Mark Ryan

The basic idea behind copying a given angle is to use your compass to sort of measure how wide the angle is open; then you create another angle with the same amount of opening.

geometry-angle-compass

Here’s the proof diagram.

geometry-copying-angle
Copying an angle.

Refer to the figure as you work through these steps:

  1. Draw a working line, l, with point B on it.
  2. Open your compass to any radius r, and construct arc (A, r) intersecting the two sides of angle A at points S and T.
  3. Construct arc (B, r) intersecting line l at some point V.
  4. Construct arc (S, ST).
  5. Construct arc (V, ST) intersecting arc (B, r) at point W.
  6. Draw line BW and you’re done.