Question

8 from unit 1, lesson 16 select all the angles of rotation that produce symmetry for this flower. a 45° b 60° c 90° d 120° e 135° f 150° g 180°

Explanation:

Step1: Count the number of petals

The flower has 8 petals.

Step2: Calculate the angle of rotational symmetry

The formula for the angle of rotational symmetry is \(\frac{360^{\circ}}{n}\), where \(n\) is the number of petals. Here \(n = 8\), so \(\frac{360^{\circ}}{8}=45^{\circ}\).
Any multiple of \(45^{\circ}\) will also produce symmetry.

• For \(45^{\circ}\): \(45^{\circ}\times1 = 45^{\circ}\)
• For \(90^{\circ}\): \(45^{\circ}\times2=90^{\circ}\)
• For \(135^{\circ}\): \(45^{\circ}\times3 = 135^{\circ}\)
• For \(180^{\circ}\): \(45^{\circ}\times4=180^{\circ}\)

Answer:

A. \(45^{\circ}\), C. \(90^{\circ}\), E. \(135^{\circ}\), G. \(180^{\circ}\)