Identifying and measuring an angle

What is an angle?

An angle is formed by two half-lines that share the same point of origin, known as the vertex. An angle is denoted by three letters, for example angle ABC, where B is always the vertex (the middle letter).

Angles are measured in degrees (symbol °) using a protractor. The protractor has two scales (from 0 to 180 in each direction): you must choose the correct one to avoid getting the measurement wrong.

The different types of angles

Type of angle	Measure	Example
Acute angle	between 0 and 90 (exactly)	45°
Right angle	exactly 90	90°
Obtuse angle	between 90 and 180 (exactly)	120°
Straight angle	exactly 180	180°

A right angle is often represented by a small square in diagrams, rather than an arc of a circle.

Common pitfall

Many pupils read the wrong scale on the protractor and confuse, for example, 40° with 140°. Tip: check whether the angle looks acute (small, tight) or obtuse (wide, open) to the naked eye before reading the number; this helps to avoid mistakes.

Practical example

If an angle measures 130°, it is obtuse because 130 lies between 90 and 180. If an angle measures 90°, it is a right angle, even if it does not appear perfectly square in a freehand drawing.