Rotational Symmetry

Turn a rectangle about its centre. After $180^{\circ }$ every vertex has moved to the opposite vertex, so the rectangle fits exactly onto its original outline.

In one full turn there are exactly two positions where it matches, at $180^{\circ }$ and at $360^{\circ }$, so its order of rotational symmetry is 2, and its angle of rotation is $360÷2=180°$.

The statement is therefore True.

Turn the triangle about its centre and count the positions where it fits exactly onto its original outline in one full turn.

It matches at $120^{\circ }$, again at $240^{\circ }$ and again at $360^{\circ }$.

That is 3 matching positions, so the order of rotational symmetry is 3 (equivalently $360÷120=3$).

The order of rotational symmetry is how many times the figure fits its own outline during one full $360^{\circ }$ turn.

If it first matches after $120^{\circ }$, it matches again every $120^{\circ }$: at $120^{\circ }$, $240^{\circ }$ and $360^{\circ }$.

So $360÷120=3$, and the order of rotational symmetry is 3.

One full turn is $360^{\circ }$, and the 8 matching positions are spaced equally around that turn.

So the angle of rotation is $360÷8=45°$.

The octagon fits onto its own outline every $45^{\circ }$: at $45^{\circ }$, $90^{\circ }$, $135^{\circ }$ and so on up to $360^{\circ }$.

Sign B, the blue roundabout sign, has three identical curved arrows spaced equally around the circle. Turning it $120^{\circ }$ about its centre leaves it looking exactly the same, so it has rotational symmetry of order 3.

Sign A has a mirror line down the middle, but the exclamation mark means no turn short of a full $360^{\circ }$ maps it onto itself.

Sign C is drawn on a regular octagon, but the word STOP inside it does not repeat, so again only a full turn brings it back.

A regular pentagon has 5 equal sides and 5 equal angles, so it fits onto its own outline 5 times in a full turn: $360÷5=72$.

A turn of $72^{\circ }$ carries each vertex exactly onto the next one, so the pentagon looks identical afterwards.

The answer is Yes.