Angle symbol (∠)

How to read it

Henry Africk’s Elementary College Geometry (CUNY) defines an angle as two rays with a common end point and gives ∠ as its symbol. An angle can be named by three points or by its vertex alone, so the angle at A between rays to B and C is ∠BAC, ∠CAB or simply ∠A; with three letters the middle one is always the vertex. OpenStax’s Contemporary Mathematics names angles the same way and allows ∠ or the measured-angle sign ∡ before the points.

Also searched as: ∠, ∡, angle ABC, angle sign, m∠, measured angle.

The angle or its size?

Books differ on how to write the size of an angle. OpenStax writes the measure with an m in front, m∡A = 40°, keeping ∠A for the angle itself. Africk writes the size straight after the name: ∠BAC = 50°. The angle is measured in degrees, written with the degree sign.

Other angle signs

Unicode encodes ∠ ANGLE (U+2220), the measured angle ∡ (U+2221), drawn with an arc across it, the spherical angle ∢ (U+2222) and the right angle ∟ (U+221F). On a diagram, OpenStax marks a right angle with a little square in the corner instead (see Perpendicular symbol (⊥)).

On engineering drawings

In a feature control frame on a technical drawing, the same ∠ is the angularity tolerance. The UK National Physical Laboratory’s guide to drawings defines angularity as the condition of a surface or axis at a specified angle, other than 90°, from a datum, so on a drawing ∠ controls a part’s angle rather than naming one. Hérigone’s first angle sign was the same mark as the less-than sign <; the version that won, Cajori notes, has its lower stroke lying flat.