Question

which of the following rotations about the center map the equilateral triangle onto itself?

150°
108°
45°
none of the above

Explanation:

Step1: Recall the rotation property of an equilateral triangle

An equilateral triangle has rotational symmetry of order 3. The formula for the angle of rotation \( \theta=\frac{360^{\circ}}{n} \), where \( n = 3 \) (the number of sides). So, \( \theta = 120^{\circ},240^{\circ},360^{\circ}\cdots\)

Step2: Check the given angles

For \(45^{\circ}\): \(360\div45 = 8\), not a factor related to the rotational symmetry of an equilateral triangle.
For \(108^{\circ}\): \(360\div108=\frac{10}{3}\), not an integer.
For \(150^{\circ}\): \(360\div150 = 2.4\), not an integer.

Answer:

None of the above