Question

question
which angle of rotation would carry an equilateral triangle onto itself?
answer
330° 240°
144° 150°

Explanation:

Step1: Find the order of rotational symmetry

An equilateral triangle has 3 equal sides and 3 equal angles. The order of rotational symmetry \(n = 3\).

Step2: Calculate the angle of rotation

The formula for the angle of rotation \(\theta=\frac{360^{\circ}}{n}\). Substituting \(n = 3\), we get \(\theta=\frac{360^{\circ}}{3}=120^{\circ}\). Multiples of \(120^{\circ}\) (i.e., \(120^{\circ}\times k\), where \(k = 1,2,3,\cdots\)) will also carry the equilateral triangle onto itself. When \(k = 2\), \(\theta=240^{\circ}\).

Answer:

\(240^{\circ}\)