Question

a regular hexagon is shown below. suppose that the hexagon is rotated counterclockwise about its center so that the vertex at o is moved to m. how many degrees does the hexagon rotate?

Explanation:

Step1: Find single vertex rotation angle

A full rotation is $360^\circ$. A regular hexagon has 6 equal vertices, so the angle between adjacent vertices from the center is $\frac{360^\circ}{6} = 60^\circ$.

Step2: Count vertex steps from O to M

Moving counterclockwise from O to M: O → N → M, which is 2 vertex intervals.

Step3: Calculate total rotation angle

Multiply the single interval angle by the number of intervals: $2 \times 60^\circ = 120^\circ$.

Answer:

$120^\circ$