Provide two different degrees of rotation less than 75 deg but greater than that will turn a regular dodecagon onto itself. A regular dodecagon will turn onto itself after a and rotation.
A regular dodecagon has 12 sides, and each angle of a regular dodecagon is 150 degrees.
To find the degrees of rotation that will turn a regular dodecagon onto itself, we need to find the numbers that are multiples of 360 degrees plus the original angle.
1. First, let's find the smallest multiple of 360 degrees that is greater than 150 degrees:
360 * 1 = 360 degrees
Since 360 degrees is too large, let's find the next multiple:
360 * 2 = 720 degrees
Now we can find the rotation angle:
Rotation angle = 720 degrees - 150 degrees = 570 degrees
Therefore, a rotation of 570 degrees will turn a regular dodecagon onto itself.
2. Let's find another smaller multiple of 360 degrees that is greater than 150 degrees:
360 * 3 = 1080 degrees
Now we can find the rotation angle:
Rotation angle = 1080 degrees - 150 degrees = 930 degrees
Therefore, a rotation of 930 degrees will also turn a regular dodecagon onto itself.
To find the degrees of rotation that will turn a regular dodecagon onto itself, we need to consider the symmetries of the shape. A regular dodecagon has 12 equal sides and 12 equal angles.
1. 30 degrees: Rotating a regular dodecagon by 30 degrees will turn it onto itself. This is because 30 degrees is a divisor of 360 degrees (the total angle measure of a regular dodecagon), so after 12 rotations of 30 degrees, the dodecagon will be in its original position.
2. 60 degrees: Rotating a regular dodecagon by 60 degrees will also turn it onto itself. Similar to the previous case, 60 degrees is a divisor of 360 degrees. Therefore, after 6 rotations of 60 degrees, the dodecagon will return to its original position.
So, a regular dodecagon will rotate onto itself after a 30-degree rotation and a 60-degree rotation.
To determine the rotations that will turn a regular dodecagon onto itself, we need to consider its rotational symmetry.
A regular dodecagon has 12 equal sides and 12 equal angles. It has rotational symmetry of order 12, which means it can be rotated by a certain angle and appear identical to its original position.
To find degrees of rotation that will turn the dodecagon onto itself, we can divide a full 360° rotation by the order of symmetry (12). This will give us equal increments of rotation.
360° / 12 = 30°
So, any rotation by multiples of 30 degrees will turn the regular dodecagon onto itself. But we need rotations that are less than 75 degrees.
First Rotation: 30°
This means rotating the dodecagon by 30 degrees will bring it back to its original position. It is less than 75° and satisfies the conditions.
Second Rotation: 60°
Rotating the dodecagon by 60 degrees will also bring it back to its original position. It is less than 75° and satisfies the conditions.
Therefore, a regular dodecagon will turn onto itself after a 30° and 60° rotation.