For every how many degrees will a nonagon have rotational symmetry
The correct answer and explanation is:
A nonagon, which is a polygon with nine sides, will have rotational symmetry every 40 degrees. This means that if you rotate a nonagon by 40 degrees, it will coincide with its original shape.
To explain further, rotational symmetry refers to the ability of a shape to be rotated around a central point and still look the same at certain angles of rotation. For a polygon with nn sides, the angle of rotation for rotational symmetry is calculated by dividing 360 degrees by the number of sides nn. In the case of a nonagon, which has 9 sides, the angle of rotation can be calculated as follows: Angle of rotation=360∘n=360∘9=40∘\text{Angle of rotation} = \frac{360^\circ}{n} = \frac{360^\circ}{9} = 40^\circ
Thus, a nonagon will match its original position after every 40-degree rotation. Since there are 9 sides in a nonagon, it will align with its original position a total of 9 times during a full 360-degree rotation. These occurrences happen at multiples of 40 degrees, such as 40°, 80°, 120°, and so on, up to 360°. Each of these positions corresponds to one of the vertices of the nonagon.
This rotational symmetry is a result of the regularity of the nonagon, meaning all its sides and angles are congruent. Because of this symmetry, the nonagon will always look the same no matter how far it is rotated, as long as the rotation is a multiple of 40 degrees. This characteristic is one of the key features of regular polygons, and it applies to all polygons where the number of sides divides evenly into 360 degrees.