In the first two quizzes, we focused on finding areas — how much paint would we need to put the shape on the side of a building? But we left something out.
While area is something we can calculate for any shape, it doesn't tell us anything about what shape we're dealing with. We can have an equilateral triangle, a wide and short triangle, or a hexagon, all with an area of square unit.
What defines a shape are its angles and the lengths of its sides.
An angle is a measure of how two lines meet. The two covers of a book closed flat make no angle with each other.
And if we rotate the front cover so it's under the back cover, we'll have spun it in a complete circle (and broken the book's spine).
Similarly, if we lift the front cover so that it points straight up, the front cover rotates through a quarter of a circle.
Though the measure of an angle is arbitrary, it's conventional to define the circle to be of rotation.