Angle transfer

If you have an angle and want to copy that angle somewhere else, you can use the angle transfer method.

How to transfer an angle

Let's start with this image:

Our task is to transpose the angle α a little higher so that the vertex of the transposed angle α' corresponds to the point A', so that it has the same orientation, and so that the lower arm lies on the line q (it is grayed out in the top image). Now we will need a compass. Draw a portion of a circle between the arms of the angle α of arbitrary radius centered at the vertex of the angle, A. Keep the radius of this circle in the compass.

Now draw the same part of the circle, of the same radius, but centred at A', the point where the vertex of the transmitted angle is to be. Where the circle intersects the line q, the point B' will be located.

Now take the distance of the line |BD|, stick the compass in the point B' and draw the circle. At the point where this circle intersects the previous part of the circle will be the point C'.

We now have all three points needed to construct the new angle B'A'C'.

Adding and subtracting angles

If you have two angles that need to be added, you can use this procedure. You take one angle, bring it to the other so that they have one common arm, and the resulting angle is made up of arms that have the two angles different:

This example shows the sum α + β. The common arm is the semi-line AC and the different arms are the semi-line AB and AD. The result is the angle BAD.

For subtraction, it works very similarly, except that you don't transfer one angle outside the other angle, but inside the angle. Then you sort of subtract the intersection of the two angles from the larger angle and you have the difference.

The picture shows the difference α − β. The red part then again highlights the resulting angle.