The angle of rotation will carry the figure onto itself is 216 degrees
The measure of angle at the center of the polygon is 360 degrees. i.e.
[tex]\theta = 360^o[/tex]
The number of sides of the regular polygon is 5. i.e.
[tex]n = 5[/tex]
So, the smallest angle of rotation that maps the polygon onto itself is
[tex] = \frac{\theta}{n}[/tex]
This gives
[tex]\alpha = \frac{360}{5}[/tex]
[tex]\alpha = 72[/tex]
Other angles that map the shape onto itself, must be a multiple of 72. i.e.
[tex]\alpha = 72, 144, 216,288,360....[/tex]
Hence, the angle of rotation will carry the figure onto itself is 216 degrees
Read more about regular polygons at:
https://brainly.com/question/1592456
