Question

n.b: you might need a transparent paper and protractor. abcdef is a regular hexagon. all angles and sides are equal. 1) what is the smallest angle of counter - clockwise rotation that matches the regular hexagon on itself. 2) what are the next three angles of counter - clockwise rotation that matches the regular hexagon to itself? __, , __

Explanation:

Step1: Recall rotation property of regular polygon

For a regular polygon with \(n\) sides, the smallest angle of rotation \(\theta\) that maps the polygon onto itself is given by \(\theta=\frac{360^{\circ}}{n}\). A hexagon has \(n = 6\) sides.

Step2: Calculate the smallest rotation angle

\(\theta=\frac{360^{\circ}}{6}=60^{\circ}\)

Step3: Find the next - three rotation angles

The rotation angles that map a regular polygon onto itself are multiples of the smallest rotation angle. So the next three angles are \(2\times60^{\circ}=120^{\circ}\), \(3\times60^{\circ}=180^{\circ}\), \(4\times60^{\circ}=240^{\circ}\)

Answer:

1. \(60^{\circ}\)
2. \(120^{\circ}\), \(180^{\circ}\), \(240^{\circ}\)