Question

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

Answer 1

The correct answer is: 180°

Explanation:
Let's consider each angle one by one:
45°: If we rotate the above figure by 45°, it will not map onto itself; rather it will make 45° angle with the correct figure.
90°: If we rotate the above figure by 90°, it will be perpendicular to the given figure.
180°: If we rotate the above figure by 180°, it will map onto itself exactly.
360°: If we rotate the above figure by 360°, it will map onto itself exactly.

However, as the question is about the least angle, hence, in this case, the correct answer is 180° (since 180° < 360°).

Answer 2

Notice that the given figure is symmetric about the centre, i.e. when the figure is divided into two equal parts, we have similar object.

For the figure to map to itself, the minimum angle rotation needed is 180 degrees.