Naming an angle

An angle is formed by two rays that have a common starting point. Think of your arm, fixed at the shoulder and turning: the shoulder is the hinge. In the book's example, rays BD and BE both start at B. The common starting point B is the vertex, and the rays BD and BE are the arms. In a drawing we show an angle with a small curve at the vertex.

Naming it: we can say Angle B. To be clearer, use one point on each arm with the vertex in the middle: Angle DBE or Angle EBD. 'Angle' is often written with the symbol ∠, so we write ∠DBE or ∠EBD. The vertex is always the middle letter.

Angles are everywhere. Open a compass or a divider: its two arms make an angle, and the vertex is where the arms are joined. Open a pair of scissors: the blades are the arms, and the vertex is the screw where they are joined.

Sometimes one letter is not enough. In your book, three rays PA, PB and PC all start at P. Now there are three angles with their vertex at P: ∠APB, ∠BPC and ∠APC. Say just '∠P' and nobody knows which one you mean. That is why ∠APB cannot be labelled ∠P.