# 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

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:

## Step 1

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

Example. Step 1

## Step 2

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

Example. Step 2

## Step 3

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

Example. Step 3

## Step 4

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

Example. Step 4