Question

determine the minimum rotation (in degrees) which will carry the following figure onto itself (where all sides and vertices will match up). round to the nearest tenth if necessary.
60
90
360
22.5
45
180

Explanation:

Step1: Recall the concept of rotational symmetry

A figure has rotational symmetry if it can be rotated by an angle \(\theta\) (\(0 < \theta\leqslant360^{\circ}\)) and map onto itself. For a non - regular polygon (a trapezoid in this case, which is not a regular polygon), we consider the general rule. A full rotation is \(360^{\circ}\).

Step2: Analyze the trapezoid

A trapezoid (a non - regular quadrilateral) has rotational symmetry of order \(1\) for non - isosceles trapezoid. But if we consider the fact that when we rotate a figure by \(360^{\circ}\), it will always map onto itself. For any non - point, non - line geometric figure, a \(360^{\circ}\) rotation will carry the figure onto itself.

Answer:

\(360\)