An example of a symmetrical angle can be found in the context of rotational symmetry. Specifically, consider the angle of rotation that leaves a shape looking unchanged.
When discussing symmetrical angles, it's important to differentiate between angles that are themselves symmetrical (i.e., bisected equally) and angles of rotational symmetry within geometric shapes. This response focuses on the latter, as implied by the reference.
Angles of Rotational Symmetry
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Definition: An angle of rotational symmetry is the smallest angle through which a shape can be rotated and still appear identical to its original orientation.
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Example: Square Imagine a square. If you rotate it by 90 degrees around its center, it looks exactly the same. Therefore, 90 degrees is an angle of rotational symmetry for a square.
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Examples in Regular Polygons:
- A regular hexagon has rotational symmetry of 60 degrees (360/6 = 60).
- A regular pentagon has rotational symmetry of 72 degrees (360/5 = 72).
- An equilateral triangle has rotational symmetry of 120 degrees (360/3 = 120).
Summary
In summary, a 90-degree angle is an example of a symmetrical angle within the context of rotational symmetry as it applies to a square. Similarly, the angles of rotational symmetry for other regular polygons are also examples.
