Question

what is the least angle measure by which this figure can be rotated so that it maps onto itself? 45° 90° 180° 360°

Explanation:

Step1: Identify rotational symmetry

The figure has rotational symmetry. We need to find the smallest angle of rotation for which it maps onto itself.

Step2: Analyze the figure

By observing the figure, we can see that it has 2 - fold rotational symmetry. The full - rotation is 360°. For a figure with 2 - fold rotational symmetry, the smallest angle of rotation $\theta=\frac{360^{\circ}}{n}$, where $n$ is the order of rotational symmetry. Here $n = 2$.
So, $\theta=\frac{360^{\circ}}{2}=180^{\circ}$

Answer:

180°