Step by step
The question
Question: what is the order of rotational symmetry of a regular pentagon?
1 Mark a corner
Put a dot on one corner, so we can follow it.
Then turn the shape about its center.
2 Turn and count
After a turn of 72°, it fits on itself again.
That is 1.
After a turn of 144°, it fits on itself again.
That is 2.
After a turn of 216°, it fits on itself again.
That is 3.
After a turn of 288°, it fits on itself again.
That is 4.
One more turn: the dot is back at the start.
That is 5.
3 The order
It fits 5 times in one full turn.
So the order is 5.
Careful!
The start and the full turn are the same place.
Count it once.
4 Check
Let's check.
One full turn is 360 degrees.
Shared by 5, each turn is 72°.
5 turns of 72 degrees make 360 degrees: one full turn.
Right!
Let's look back.
First: mark a corner.
Then: turn and count.
Then: the order.
Last: check.