Question

analyzing rotational symmetry
if this regular decagon is rotated counterclockwise by 3 times the smallest angle of rotation, which vertex will be in the top position?

Explanation:

Step1: Find smallest rotation angle

For a regular decagon, the smallest angle of rotation is $\frac{360^{\circ}}{10}=36^{\circ}$.

Step2: Calculate actual rotation angle

The decagon is rotated by 3 times the smallest angle, so the rotation angle is $3\times36^{\circ} = 108^{\circ}$.

Step3: Determine new vertex position

Starting from vertex B at the top - position initially. A $108^{\circ}$ counter - clockwise rotation moves the vertex 3 positions counter - clockwise (since $108\div36 = 3$). So the new vertex at the top is E.

Answer:

E