Question

3
select the correct image.
which figure will rotate onto itself in 45° increments?

Explanation:

Step1: Recall Rotational Symmetry

A regular polygon with \( n \) sides has a rotational symmetry of \( \frac{360^\circ}{n} \). We need a figure where \( \frac{360^\circ}{n}=45^\circ \), so solve \( n = \frac{360^\circ}{45^\circ}=8 \). So we need a regular octagon (8 - sided polygon).

Step2: Identify the Octagon

Among the figures, the regular octagon (8 equal sides/angles) will rotate onto itself every \( 45^\circ \) (since \( 360\div8 = 45 \)). Looking at the images, the figure with 8 sides (the octagon, likely the third in top row or one of the bottom with 8 sides) is the correct one. Assuming the octagon (8 - sided) is the one that fits, as it has \( n = 8 \), so rotational increment \( 45^\circ \).

Answer:

The figure with 8 sides (regular octagon, e.g., the third figure in the top row or the appropriate octagonal figure)