Final Answer:
The angle of rotation counterclockwise about p that maps d to e is 60 degree.
The correct answer is c) 60°.
Step-by-step explanation:
To solve this question, let's first recall some properties of a regular hexagon:
1. A regular hexagon has six sides of equal length and six angles of equal size.
2. Each interior angle in a regular hexagon is 120 degrees because the sum of interior angles in any hexagon is (6-2)*180 = 720 degrees, so each interior angle is 720 degrees / 6 = 120 degrees.
3. The exterior angles are formed by extending the sides of the hexagon. Since each interior angle is 120 degrees, each exterior angle of a regular hexagon will be 180 degrees - 120 degrees = 60 degrees (because the interior and exterior angles are supplementary and add up to 180 degrees).
Now, let's focus on the rotation part of the problem. We are looking for the angle of rotation counterclockwise about point P that maps point D to point E.
Let's visualize the steps in the process:
- Imagine starting at point D.
- Since E is the next vertex in the counterclockwise direction, we need to rotate to E from D.
- Point E is exactly one side away from point D in the hexagon, thus one step counterclockwise.
Knowing that one exterior angle equals 60 degrees and that this accounts for the rotation needed to move from one vertex to the adjacent one in a hexagon, we can say that the angle of rotation counterclockwise about point P that maps point D to point E is equal to one exterior angle.
Therefore, the angle of rotation from D to E counterclockwise is 60 degrees.
The correct answer is c) 60°.