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Yes. Mathematicians measure angles in units called a radian which is the ratio of two lengths: the radius of a circle and the length of the subtended arc. Since it is a ratio of two lengths it has 0-dimensions. Even though the degree is defined in a different way, it is directly related to a radian (180 deg = pi radians) and so has no dimensions.

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What is the angle through which the figure turns?

The angle through which a figure turns is typically measured in degrees or radians, representing the amount of rotation around a point. For example, a full rotation is 360 degrees or (2\pi) radians. The specific angle can be determined by the difference between the initial and final positions of the figure. If the figure turns clockwise, the angle is considered positive, while counterclockwise turns are often considered negative.


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If you can rotate (or turn) a figure around a center point by fewer than 360° and the figure appears unchanged, then the figure has rotation symmetry. The point around which you rotate is called the center of rotation, and the smallest angle you need to turn is called the angle of rotation. This figure has rotation symmetry of 72°, and the center of rotation is the center of the figure:


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