Question

What is the angle of the clockwise rotation in degrees

Answer 1

The figure is a regular pentagon, so all its internal angles are equal. So the first step is to find the value of the internal angle, that will also be the minimum rotation angle to have a new figure in the same orientation.

The formula to find the internal angle of a regular polygon is:

`a_i=((n-2)\cdot180)/(n)`

Using n = 5, we have:

`a_i=((5-2)\cdot180)/(5)=(3\cdot180)/(5)=(540)/(5)=108\degree`

The internal angle is 108°.

A rotation of 108° would make all vertices move one position (to the position of the next vertix).

We can see that point A moved two positions (from the left vertix to the right vertix), so the rotation angle is 2 times the internal angle:

`\text{rotation angle}=2\cdot108=216\degree`

So the correct option is B.