Question

youve now likely noticed a pattern with the regular polygons. lines of symmetry depend on whether the shape has an even or odd number of sides. the minimum angle of rotation also depends on the number of sides. exercise #6: a regular hexagon (6 sides), octagon (8 sides) and nonagon (9 sides) are shown. sketch all lines of symmetry and give the minimum angle of rotation about the center point that would map the figure onto itself. (a) hexagon (b) octagon (c) nonagon

Explanation:

Step1: Fórmula para el ángulo de rotación

El ángulo mínimo de rotación \( \theta \) de un polígono regular con \( n \) lados se calcula con la fórmula \( \theta=\frac{360^{\circ}}{n} \).

Step2: Cálculo para el hexágono (\( n = 6 \))

Sustituimos \( n = 6 \) en la fórmula: \( \theta=\frac{360^{\circ}}{6}=60^{\circ} \).

Step3: Cálculo para el octágono (\( n = 8 \))

Sustituimos \( n = 8 \) en la fórmula: \( \theta=\frac{360^{\circ}}{8}=45^{\circ} \).

Step4: Cálculo para el nonágono (\( n = 9 \))

Sustituimos \( n = 9 \) en la fórmula: \( \theta=\frac{360^{\circ}}{9}=40^{\circ} \).

Answer:

• (a) Hexágono: \( 60^{\circ} \)
• (b) Octágono: \( 45^{\circ} \)
• (c) Nonágono: \( 40^{\circ} \)