Question

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

Explanation:

Step1: Find central angle per vertex

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

Step2: Count vertex steps from L to J

Count counterclockwise from L: L→K→J, which is 2 vertex intervals.

Step3: Calculate total rotation degrees

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

Answer:

$120$