Types of Angles

In one line: An angle is the amount of turn between two straight lines that meet at a point, and we name it by its size: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°) or reflex (between 180° and 360°).

Why it works

Angles are everywhere: in the corners of rooms, the hands of a clock, ramps, roofs and the shapes you draw in maths. Knowing the types of angles lets you describe shapes clearly, estimate sizes before you measure, and check whether a protractor reading makes sense. Angles are measured in degrees (written °), and a full turn all the way round is 360°. The point where the two lines meet is called the vertex, and the two lines are called the arms.

Think of it like: Think of opening a door. When it is shut, there is no turn at all. Open it a little and the gap makes an acute angle. Open it until it makes a perfect square corner with the wall and that is a right angle (90°). Swing it wider and you get an obtuse angle. If it could swing flat against the same wall it would make a straight line, a straight angle of 180°. (Where this breaks: A real door stops at its hinge, but angles can keep turning past 180° all the way to a full turn of 360°, and those bigger turns are reflex angles. Also, a wider door does not make a bigger angle: the size of an angle depends only on the amount of turn, not on how long the arms are.)

Worked example

At 4 o'clock, what is the smaller angle between the hands of a clock, and what type of angle is it? What type is the larger angle going the other way round?

A full turn round the clock face is 360°, and there are 12 hour marks, so each gap between hour marks is 360° ÷ 12 = 30°.
At 4 o'clock the minute hand points at 12 and the hour hand points at 4, which is 4 gaps apart.
4 × 30° = 120°, so the smaller angle is 120°.
120° is more than 90° but less than 180°, so it is an obtuse angle.
The larger angle the other way round is 360° − 120° = 240°, which is between 180° and 360°, so it is a reflex angle.

Answer: The smaller angle is 120°, an obtuse angle; the larger angle is 240°, a reflex angle.

Common mistakes

Thinking an angle with longer arms is bigger – the fix is to look only at the amount of turn between the arms, not their length.
Reading the wrong scale on a protractor (for example getting 140° instead of 40°) – the fix is to first decide if the angle looks acute or obtuse, then pick the reading that matches.
Calling a 180° angle obtuse – the fix is to remember obtuse stops just before 180°, and exactly 180° is a straight angle.
Forgetting the outside angle – the fix is to remember that every pair of lines makes two angles, and the larger one (more than 180°) is the reflex angle.

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What type of angle measures 65°?

Questions parents ask

What year do kids learn the types of angles?

In the UK, children meet right angles in Year 3, compare acute and obtuse angles in Year 4, and learn reflex angles and measuring with a protractor in Year 5. In Australia this is mainly covered in Years 4 to 6, and in the US students identify and measure acute, right and obtuse angles in Grade 4.

How can I help my child learn types of angles at home?

Go on an angle hunt: look for right angles in door frames and books, acute angles in a slice of pizza, and obtuse angles in an open laptop. You can also use an analogue clock and ask your child to name the angle between the hands at different times.

What is a reflex angle?

A reflex angle is bigger than 180° but smaller than 360°. It is the 'outside' angle when two lines meet, going the long way round, and you can find it by taking the smaller angle away from 360°.

How can my child remember acute and obtuse?

Many children remember that an acute angle is small and 'a-cute' little angle, while obtuse is the wider, more open one. Using a corner of a sheet of paper as a right-angle checker helps too: anything smaller is acute, anything wider (but not flat) is obtuse.