Find the angle of rotational symmetry for a regular pentagon.
Answer (1)
Understand that rotational symmetry refers to the angle by which a shape can be rotated and still look the same.
Recall the formula for calculating the angle of rotational symmetry for a regular polygon: n 360 , where n is the number of sides.
Apply the formula to a regular pentagon ( n = 5 ) to find the angle of rotational symmetry: 5 360 = 72 .
Conclude that the angle of rotational symmetry for a regular pentagon is 72° .
Explanation
Understanding Rotational Symmetry A regular pentagon has 5 equal sides and 5 equal angles. When we rotate a regular pentagon about its center, it will look the same after a certain angle of rotation. This angle is called the angle of rotational symmetry. To find this angle, we divide the total degrees in a circle (360°) by the number of sides (or vertices) of the regular pentagon.
Formula for Angle of Rotational Symmetry The formula for the angle of rotational symmetry of a regular n-sided polygon is given by: n 360 In this case, we have a regular pentagon, so n = 5 .
Calculating the Angle Now, we can calculate the angle of rotational symmetry for the regular pentagon: 5 360 = 72 So, the angle of rotational symmetry for a regular pentagon is 72 degrees.
Final Answer Therefore, the angle of rotational symmetry for a regular pentagon is 72°.
Examples
Rotational symmetry is useful in various fields, such as art, design, and engineering. For example, when designing a snowflake or a gear, understanding rotational symmetry helps ensure that the object looks balanced and functions correctly from all angles. In architecture, knowing the angles of rotational symmetry can help in creating aesthetically pleasing and structurally sound buildings.
