What is the smallest value of an angle, , by which a regular pentagon should be rotated about its center x so that it carries onto itself?

Explanation:

Given

Shape: Regular Pentagon

Required

Determine the minimum value of x

A pentagon has 5 sides and 1 complete rotation of a pentagon about its centre is 360 degrees

i.e.

The angle of rotation (x) is then calculated as:

Substitute values for 1 rotation and sides

The above is the minimum value of rotation.

As a bonus

Other possible angle of rotation must be in multiples of 72

i.e.

This means that when the pentagon is rotated in any of the above angles of rotation, it will be carried onto itself.

d. stage 4

explanation:

the existence of some kind of demographic transition is widely accepted in the social sciences because of the well-established historical correlation linking dropping fertility to social and economic development.[1] scholars debate whether industrialization and higher incomes lead to lower population, or whether lower populations lead to industrialization and higher incomes. scholars also debate to what extent various proposed and sometimes inter-related factors such as higher per capita income,lower mortality, old-age security, and rise of demand for human capital are involved.[2]