Since the polygon shown is a regular one, a rotation will carry it onto for every angle that makes a vertex to the place of another vertex.
So, we can fisrt figure the angle we need to rotate to get a vertex onto the next one, that is, we want to find the following angle:
We know tha the polygon is regular, so this angles is the same as the angles between the other consecutive vertexes. Since we have 5 vertexes, this angle is 1/5 of the role 360°. So, this angles is:
[tex]\frac{360\degree}{5}=72\degree[/tex]
That means that a rotation of 72° will always endup in the same figure.
This also means that a rotation of any multiple of 72° will also end up in the same figure.
Thus, we just have to check which alternative is a multiple of 72°.
- 60° isn't a multiple, because it is lower.
- 108° also isn't because the 2*72 = 144, which is higher than 108°.
- 540° isn't, because 7*72 = 504 and 576, which passed through 540°
- 216° is a multiple because 3*72 = 216 exactly.
This means that if we rotate the figure by 210° it will end up in the same figure.
So, the correct alternative is the last one: 216°.
