We want to determine whether the figure has rotational symmetry. To do so, remember that the octagon can be described as a four-pointed star. Now, we will draw segments between opposite vertices of the star.
Notice that if we turn it by 90^(∘), the octagon looks the same as before the rotation. This means that a rotation of 90^(∘) will map it onto itself. Now, let's apply a rotation of 180 ^(∘).
As we can see, the rotation of 180^(∘) will also work. This means that the octagon has a rotational symmetry, and rotations of 90^(∘) and 180^(∘) map it onto itself.
