Question

1. list the angles of rotation for which the figures have rotational symmetry.

a. 90°, , and
b. and 240°

Explanation:

Step1: Recall the formula for rotational symmetry angle

The formula for the angle of rotational symmetry is \(\frac{360^{\circ}}{n}\), where \(n\) is the number of times the figure coincides with itself in a full - \(360^{\circ}\) rotation.

Step2: Analyze figure a

For the four - pointed star (figure a), \(n = 4\). The angles of rotation are \(k\times\frac{360^{\circ}}{4}\), where \(k = 1,2,3\).
When \(k = 1\), the angle is \(90^{\circ}\); when \(k = 2\), the angle is \(180^{\circ}\); when \(k = 3\), the angle is \(270^{\circ}\)

Step3: Analyze figure b

For an equilateral triangle (figure b), \(n=3\). The angles of rotation are \(k\times\frac{360^{\circ}}{3}\), where \(k = 1,2\).
When \(k = 1\), the angle is \(120^{\circ}\); when \(k = 2\), the angle is \(240^{\circ}\)

Answer:

a. \(180^{\circ}\), \(270^{\circ}\)
b. \(120^{\circ}\)