Question

select the correct image. which figure will rotate onto itself in 45° increments?

Explanation:

Step1: Recall the formula for rotational symmetry

The formula for the angle of rotational symmetry of a regular polygon is $\frac{360^{\circ}}{n}$, where $n$ is the number of sides. We need to find a figure where $\frac{360^{\circ}}{n}=45^{\circ}$.

Step2: Solve for $n$

From $\frac{360^{\circ}}{n}=45^{\circ}$, we can solve for $n$ by cross - multiplying: $n=\frac{360^{\circ}}{45^{\circ}} = 8$. So we are looking for an 8 - sided figure (octagon).

Answer:

The octagon (the third figure in the top row)