What is the least angle measure by which this figure can be rotated so that it maps onto itself?

45°
90°
180°
360°

Solution:

Let us consider each angle one by one and find the rotational symmetry in each case.

1. 45° - If the figure is rotated about 45° it will not map onto itself.

2. 90° - If the figure is rotated about 90°, it will be perpendicular to the given figure.

3. 180° - If the figure is rotated about 180°, it will map onto itself correctly.

4. 360° - If the figure is rotated about 360°, it will map onto itself correctly.

As the question is about the least angle, 180° < 360°.

Therefore, the least angle measure is 180°.

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

Summary:

The least angle measure by which this figure can be rotated so that it maps onto itself is 180°.