Angles: types, notation and measuring

In a nutshell

Angles can be categorised as acute, right-angled, obtuse or reflex. Angles can be measured with a protractor and they can be represented by three-letter notation.

Types of angles

NAME	ANGLE RANGE	DIAGRAM
Acute	less than $90\degree$
Right angle	$90\degree$
Obtuse	between $90\degree$ and $180\degree$
Reflex	between $180\degree$ and $360\degree$

Measuring angles with a protractor

An angle can be measured using a protractor. Line up the base line of the protractor with one of the lines forming the angle, with the cross of the protractor on top of the point of the angle. There are two scales on the protractor, one on the inside circle and one on the outside. Make sure to read the correct scale by finding where $0\degree$ lines up with one of the lines forming the angle.

Example 1

Find the size of the angle shown.

Maths; Angles and geometry; KS4 Year 10; Angles: types, notation and measuring

Position the protractor on the angle and read the inside circle.

Maths; Angles and geometry; KS4 Year 10; Angles: types, notation and measuring

The angle is $\underline{40\degree}$ .

Three-letter angle notation

Three-letter angle notation is used when there are multiple angles on a diagram. The angles are written in the form $\angle ABC$ , where the angle is at $B$ , and the lines forming the angle end at points $A$ and $C$ .

Example 2

Describe the right angle below in three-letter notation.

Maths; Angles and geometry; KS4 Year 10; Angles: types, notation and measuring

The right angle is at $C$ and the lines forming the angle go to points $A$ and $B$ .

Therefore, the right angle is $\underline{\angle ACB}$ .