In mathematics, the angle of rotation is a measurement of the amount, the angle, that afigure is rotated about a fixed point, often the center of a circle.
For example, the carts on a Ferris wheel move along a circle around the center point of that circle. If a cart moves around the wheel once, the angle of rotation is 360 degrees. If the cart was stuck halfway, at the top of the wheel, at that point its angle of rotation was only 180 degrees.
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An octagon may have 1, 2, 4 or 8 angles of rotation.
360⁰
45
4
Right angles are ninety degree angles. That is equal to one quarter of a complete rotation.