Answer:
The minimum angle it must rotate by is 45°
Step-by-step explanation:
This is basically asking you "by how much should you rotate an octagon so that it looks as if you didn't rotate it at all? "
We have to rotate the octagon such that after rotation the vertices are in the similar positions. In an octagon the angle between two consecutive vertices is 45°, so if we rotate our octagon by 45° (let's say we rotate it clockwise), a vertex that was to the left of the vertex here will now be here, and the vertex that was here will have moved 45° clockwise into the position of the vertex that was after it: vertices just exchange positions; therefore, there is no way you can tell whether you rotated your octagon.
