What is the order of rotational symmetry of a regular pentagon? ? 2 ?
The Correct Answer and Explanation is:
The order of rotational symmetry of a regular pentagon is 5.
Explanation:
Rotational symmetry refers to the number of times a shape matches its original position in one full rotation of 360 degrees. For a regular polygon, such as a regular pentagon, the order of rotational symmetry is determined by how many times you can rotate the shape so that it coincides with its original position before completing a full 360-degree rotation.
A regular pentagon has five sides and five vertices, all of equal length and angles. To understand the rotational symmetry, we divide 360 degrees (the total angle of a full rotation) by the number of sides or vertices in the polygon:360∘5=72∘\frac{360^\circ}{5} = 72^\circ5360∘=72∘
So, every time you rotate the pentagon by 72 degrees, it coincides with its original position. Since there are five such rotations (one for each side or vertex), the order of rotational symmetry is 5. These rotations are at 72 degrees, 144 degrees, 216 degrees, 288 degrees, and finally, after 360 degrees, the pentagon returns to its original position.
Thus, the regular pentagon has 5 distinct positions that it maps onto itself during a 360-degree rotation. This makes its order of rotational symmetry 5.
In simpler terms, you can rotate a regular pentagon five times by 72 degrees each time, and it will look the same in each of those positions.
