A regular decagon is a ten-sided polygon. To determine the smallest angle of rotation that would map the decagon onto itself, you need to divide 360 degrees by the number of sides.
1. A full rotation around a circle is 360 degrees.
2. Because the decagon has 10 sides, the angle required to rotate the decagon onto itself is [tex]\( \frac{360°}{10} \)[/tex].
Performing this division, we get:
[tex]\[ \frac{360°}{10} = 36° \][/tex]
So, the angle of rotation that would carry a regular decagon onto itself is 36°.
Given the choices:
- 252°
- 45°
- 150°
- 60°
None of these angles are correct based on the solutions provided. The correct answer, 36°, is unfortunately not listed among the choices.
