Subsequent rotations have the following property:

 

Several subsequent rotations of point M about center O are equivalent to one rotation, the magnitude of which is equal to the sum of the magnitudes of these rotations.

 

 

The angles of rotation greater than 180° (–180°) can be represented as the sum of angles formed by several subsequent rotations.

 

For example, a rotation angle equals 254°. This means that the angle could be formed by subsequent rotations by 180° and 74°.

For example, a rotation angle equals -254°. This means that the angle could be formed by subsequent rotations by -180° and -74°.

For example, a rotation angle equals -254°. This means that the angle could be formed by subsequent rotations by

Углы поворота, которые больше 180

 

 

A mobile ray (the terminal side of the angle) can complete any number of turns, which allows us to consider angles of an arbitrary value.

For example, a rotation angle equals 1080°. This means that the ray completed 3 full circles:

Углы поворота, которые больше 180

To understand this property, let us consider the following example.

 

Step 1

 

Assume that point M rotates by 30° about point O.

Углы поворота, которые больше 180

Example. Step 1

Step 2

 

Then, let us rotate this point by 40° (this rotation is denoted as a point in the figure).

Углы поворота, которые больше 180

Example. Step 2

Step 3

 

After that, let us rotate this point by −60°.

Углы поворота, которые больше 180

Example. Step 3

Step 4

 

The figure shows that as a result, point M completes a rotation that corresponds to angle KOM equal to:

The angles of rotation greater than 180°

Углы поворота, которые больше 180

Example. Step 4