Provide two different degrees of rotation less than 75° but greater than 0° that will turn a regular dodecagon onto itself.(1 point) A regular dodecagon will turn onto itself after a ° and ° rotation.
A regular dodecagon has 12 sides, so it can be turned onto itself after a 30° and a 60° rotation.
A regular dodecagon has 12 sides, so it will turn onto itself after a certain degree of rotation. We need to find two degrees of rotation that are less than 75° but greater than 0°.
One possible degree of rotation is 30°. After rotating the dodecagon by 30°, it will align with its original position.
Another possible degree of rotation is 60°. After rotating the dodecagon by 60°, it will also align with its original position.
Therefore, a regular dodecagon will turn onto itself after a 30° and 60° rotation.
To find the degrees of rotation that will turn a regular dodecagon onto itself, we need to consider its rotational symmetry.
A regular dodecagon has 12 sides, and its rotational symmetry is determined by dividing 360° (a full circle) by the number of sides, which in this case is 12.
So, each interior angle of a regular dodecagon measures 360° / 12 = 30°.
To find a degree of rotation less than 75° but greater than 0°, we can multiply the interior angle by a whole number. Here are two options:
1. A 2-fold rotation: Multiplying the interior angle by 2 gives us 30° * 2 = 60°. So, a 60° rotation will turn the regular dodecagon onto itself.
2. A 3-fold rotation: Multiplying the interior angle by 3 gives us 30° * 3 = 90°. However, this value exceeds the given requirement (less than 75°). Therefore, let's find a smaller angle. Subtracting 360° from 90° gives us 90° - 360° = -270°. Since we are working with positive angles, we can add 360° to -270° to find the equivalent positive angle: -270° + 360° = 90°. Therefore, a 90° rotation (or -270°, which is equivalent) will also turn the regular dodecagon onto itself.
Hence, a regular dodecagon will turn onto itself after a 60° and a 90° (or -270°) rotation.