Naming Angles
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- Naming Angles - Video - How to Name an Angle Watch
Theory
An angle is made by two arms that meet at a point called the vertex. Name it with three capital letters, with the vertex in the middle: \(\angle ABC\). This Year 7 maths page explains intervals, rays and lines, naming angles, adjacent and reflex angles, and the marks used on diagrams.
Points are named with capital letters. An interval \(AB\) stops at \(A\) and at \(B\). A ray \(AB\) starts at \(A\), passes through \(B\) and goes on forever. A line \(AB\) goes on forever in both directions.
An angle has a vertex (the corner) and two arms. To name it, write a point on one arm, then the vertex, then a point on the other arm: \(\angle ABC\). \(\angle CBA\) is the same angle. The arc between the arms shows which angle is meant.
The one-letter name \(\angle B\) is fine only when there is just one angle at \(B\).
Adjacent angles share a vertex and an arm, and sit side by side without overlapping. Reflex \(\angle ABC\) is the angle the long way round, outside the arms.
Conventions: a small square shows a right angle (\(90^\circ\)). Matching tick marks show equal intervals, and matching arcs show equal angles.
Naming rules:
| Figure | Name | Note |
|---|---|---|
| interval | \(AB\) | stops at both ends |
| ray | ray \(AB\) | starts at \(A\) (the first letter) |
| line | line \(AB\) | goes on both ways |
| angle | \(\angle ABC\) or \(\angle CBA\) | vertex in the middle |
| reflex angle | reflex \(\angle ABC\) | the long way round |
How to name an angle
- Find the vertex (where the arc is).
- Pick a point on each arm.
- Write arm point, vertex, arm point: the vertex goes in the middle.
- Add “reflex” if the arc goes the long way round.
The arc is at \(K\), so \(K\) is the vertex. \(\angle KJL\) would be wrong: its middle letter is \(J\).
Vertex \(K\); arms \(KJ\) and \(KL\); \(\angle JKL\) (or \(\angle LKJ\)).
The vertex is \(B\); the arms go to \(A\) and \(C\).
\(\angle x = \angle ABC\) (or \(\angle CBA\))
The vertex is \(B\). One arm goes along the line to \(C\); the other goes down to \(E\).
\(\angle x = \angle CBE\) (or \(\angle EBC\))
(i) the angle with one arc
(ii) the angle with two arcs
(iii) the angle they make together
Every angle here has vertex \(O\) in the middle. \(\angle AOB\) and \(\angle BOC\) are adjacent: they share arm \(OB\).
(i) \(\angle AOB\)
(ii) \(\angle BOC\)
(iii) \(\angle AOC\)
One arc: vertex \(Q\), arms \(QS\) and \(QR\). Two arcs: vertex \(P\); the lower arm runs \(P \to S \to R\), so \(S\) or \(R\) can name it.
\(\angle SQR\); \(\angle QPR\) or \(\angle QPS\)
(i) Is \(\angle KML\) adjacent to \(\angle KMN\)?
(ii) Name the angle adjacent to \(\angle KML\) with arm \(ML\).
(iii) Name the angle shown dashed.
(i) Both have vertex \(M\) and arm \(MK\), but \(\angle KML\) sits inside \(\angle KMN\): they overlap.
(ii) \(\angle LMN\) shares arm \(ML\) and sits beside \(\angle KML\).
(iii) The dashed arc goes the long way round from \(MK\) to \(MN\).
(i) No
(ii) \(\angle LMN\)
(iii) reflex \(\angle KMN\)
Pair the first arm with the \(4\) after it, the second with the \(3\) after it, and so on.
| \(4 + 3 + 2 + 1\) | \(=\) | \(10\) |
There are \(10\) angles.
Common pitfalls
Frequently asked questions
What is the vertex of an angle?
The point where the two arms meet. In \(\angle ABC\) it is \(B\).
How do you name an angle with three letters?
Point on one arm, then the vertex, then a point on the other arm: \(\angle ABC\).
What is the difference between a ray and a line?
A ray starts at a point and goes on one way; a line goes on forever both ways.
What are adjacent angles?
Angles that share a vertex and an arm and sit side by side without overlapping.
What does a small square on an angle mean?
The angle is a right angle, \(90^\circ\).