Question

A regular decagon is rotated in degrees about its center carrying the decagon onto itself. the value of n could be

Answer 1

`n = 6, 72, 108, 144, 180, 216, 252, 288, 324, 360.....`

Explanation:

Given:

`Shape: Decagon`

Required

Determine the value of n

For a decagon:

`Sides = 10`

`Complete\ Rotation = 360\°`

First, we need to determine the angle of each rotation.

This is calculated by dividing the complete rotation with number of sides

`Angle = (360)/(10)`

`Angle = 36`

Next, we calculate the possible value of n.

Since there is no option, the general rule is that the possible value of n must be a multiple of angle of each rotation i.e. 36

Hence, n could be either of the following:

`n = 6, 72, 108, 144, 180, 216, 252, 288, 324, 360.....`