Leo+DadMade for Leo
Language, Notation and Conventions of Geometry
Rung 2 of 2 · The method

Classifying and Naming Angles

Two skills that you'll use in every single angle question from here on: spot what type of angle it is from its size, and write its name correctly with ∠ and three letters.


PractiseDrag the angle open and shut to watch its type change, then have a go at the "name this angle" quiz underneath.
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There are two jobs here. First, classify an angle — say what type it is just from its size. Second, name an angle correctly. Both are quick once you know the rules.

Classify by Size

Every angle gets a name based on how open it is. Learn these five and you've got the lot:

Acute — less than 90°, a sharp little angle. Right — exactly 90°, the corner of a page (this is the one marked with the little square). Obtuse — between 90° and 180°, wider than a right angle but not yet a straight line. Straight — exactly 180°, the two arms make one straight line. Reflex — more than 180° (and less than 360°), the big way round.

Say it plainly: acute < 90° < obtuse < 180° (straight) < reflex. A right angle (90°) and a straight angle (180°) are the two exact ones; everything else lives between them.

Name It with ∠ and Three Letters

To name an angle you write then three points, with the vertex in the middle. If the corner is at B and the arms reach out to A and C, the angle is ∠ABC (and ∠CBA is the same angle — just read the other way). The two outside letters can swap; the middle one can't.

A Worked One

Say a diagram shows a corner at point Q, with one arm going to P and the other to R, and you measure the opening as 130°. Job one: 130° is between 90° and 180°, so it's an obtuse angle. Job two: vertex Q goes in the middle, so it's ∠PQR. Put it together: ∠PQR is an obtuse angle of 130°.

The one trap: the vertex letter must be in the middle. ∠ABC means the corner is at B — not at A. Writing the vertex first (or using only two letters when there are several angles at that point) is the most common slip, and it changes which angle you mean entirely.

When Two Letters Is Enough — and When It Isn't

You'll sometimes see an angle written with just one letter, like ∠B, when there's only one angle at that point and there's no chance of confusion. But the moment several angles share a vertex, you must use all three letters so it's crystal clear which one you mean. When in doubt, use three.

Us, Thinking Out Loud

Could you sort acute, right, obtuse, straight and reflex into order without peeking?

Why does the vertex have to be the middle letter — what goes wrong if it isn't?