Question

What is the name of the regular polygon that when rotated 45°, the polygon is mapped onto itself

Answer 1

The regular polygon that maps onto itself when rotated by 45° is an octagon, as it has eight sides and an octagon's full rotation of 360° can be fractioned into 45° segments.

Step-by-step explanation:

The question is asking about the name of a regular polygon that can be mapped onto itself when it is rotated by 45°. A polygon that has this property is one that has symmetrical rotation where 45° is a fraction of 360°, which is the number of degrees in a full rotation. The only regular polygon that fits this property is the octagon. An octagon has eight sides, and when you divide the full rotation of 360° by eight, you get 45°. Therefore, an octagon will map onto itself every 45° when rotated.

Answer 2

A regular polygon that is mapped onto itself when rotated 45 degrees is called a square. A square has four equal sides and four equal angles, and when it is rotated by 45 degrees, it retains its original shape.