Geometry · Lesson 6 of 18

Angles

An angle measures an amount of turn. Full, half and quarter turns are 360, 180 and 90 degrees, and the size of an angle gives it a name.

Primary
Updated 14 November 2026

What you will learn

Say what an angle is and where its vertex is.
Link turns to degrees.
Name acute, right, obtuse, straight and reflex angles.

Before you start: you should know quarter, half and full turns and what a right angle looks like. See Position, Direction and Turns and Lines, Segments, Parallel and Perpendicular.

The idea

An angle measures how far one line has turned away from another around a shared point, called the vertex. We usually measure angles in degrees ( $^\circ$ ). One full turn is $360^\circ$ , a number chosen by ancient Babylonian astronomers because it divides neatly by $2, 3, 4, 5, 6, 8, 9, 10, 12$ and many more.

A quarter turn is 90 degrees, a half turn is 180, three quarters is 270 and a full turn is 360.

Types of angle

The size of the angle gives it a name.

An acute angle is less than 90 degrees. This one is 40 degrees.

A right angle is exactly 90 degrees. The small square marks it.

An obtuse angle is between 90 and 180 degrees. This one is 130 degrees.

A reflex angle is between 180 and 360 degrees. This one is 250 degrees.

A straight angle is exactly $180^\circ$ , a half turn that makes a straight line.

Name	Size
Acute	less than $90^\circ$
Right	exactly $90^\circ$
Obtuse	between $90^\circ$ and $180^\circ$
Straight	exactly $180^\circ$
Reflex	between $180^\circ$ and $360^\circ$

Comparing angles

An angle’s size does not depend on how long its arms are. It only depends on the amount of turn between them.

Worked examples

Example 1: Name the angle

Name angles of $45^\circ$ , $90^\circ$ , $120^\circ$ and $200^\circ$ .

$45^\circ$ is less than $90^\circ$ , so acute.
$90^\circ$ is a right angle.
$120^\circ$ is between $90^\circ$ and $180^\circ$ , so obtuse.
$200^\circ$ is more than $180^\circ$ , so reflex.

Answer: acute, right, obtuse, reflex.

Example 2: A turn

You face north and turn clockwise through a quarter turn. Which way do you face, and how many degrees did you turn?

A quarter turn is $90^\circ$ .
Clockwise from north is east.

Answer: east, after turning $90^\circ$ .

Example 3: A clock

How many degrees does the minute hand turn from $12$ to $4$ ?

The clock has $12$ numbers around a full turn of $360^\circ$ , so each number is $360 \div 12 = 30^\circ$ .
From $12$ to $4$ is $4$ numbers: $4 \times 30 = 120$ .

Answer: $120^\circ$

Tip: a quick check is to compare with a right angle. Is it smaller, the same or bigger?

Why it matters

Angles are everywhere in design and navigation. Pilots and sailors steer by bearings, architects specify roof pitches, and snooker players line up shots using angles of reflection. The next lessons show how to measure angles and how to find missing ones.