To determine which rotations turn a regular triangle onto itself, we need to consider the symmetries of an equilateral triangle. A regular triangle (equilateral triangle) has rotational symmetries that occur at specific angles.
The angles that allow a regular triangle to map onto itself are multiples of \( \frac{360}{3} = 120 \) degrees, which corresponds to the three vertices of the triangle.
The relevant rotations that turn the triangle onto itself are:
- \( 0^\circ \) (or \( 360^\circ \))
- \( 120^\circ \)
- \( 240^\circ \)
Now let's check the given options:
- 45 – No
- 60 – No
- 90 – No
- 120 – Yes
- 135 – No
- 180 – No
- 225 – No
- 240 – Yes
- 270 – No
- 315 – No
- 360 – Yes (as it is equivalent to a full rotation)
Thus, the rotations that turn a regular triangle onto itself are:
- 120
- 240
- 360
So the correct answers are 120, 240, and 360.