Topics · Primary Maths · Angles
Angles: acute, right, obtuse, straight and reflex
An angle measures a turn, not a length. How long you draw the two arms changes nothing — only how far one has swung from the other.
- 274 exam papers analysed
- appears in 71% of P4 Maths papers
- ~4 min read
01 What an angle actually measures
Two straight lines meeting at a point make an angle. The angle is the size of the turn between them, measured in degrees and written with a small circle: 45°.
This is the part that trips people up: the length of the arms makes no difference. Draw the same angle with arms twice as long and it is still the same angle. Only the amount of turn counts.
A full turn all the way round is 360°. Everything else is a fraction of that — half a turn is 180°, a quarter turn is 90°.
02 The five kinds
They are named by size alone, and the boundaries are exactly 90°, 180° and 360°. Learn them as a number line rather than as five separate pictures — an angle is acute until it reaches 90°, and obtuse until it reaches 180°.
03 How to tell them apart
One comparison, against a right angle, settles it. The corner of any piece of paper is a right angle, which is why it is the thing to hold up against a drawing when you are unsure.
- Smaller than a square corner? It is acute. Between 0° and 90°.
- Exactly a square corner? It is right. Exactly 90°, and marked with a small square instead of a number.
- Bigger than a square corner but less than a straight line? It is obtuse. Between 90° and 180°.
- A straight line? It is straight. Exactly 180°.
- Bent back past straight, so you measure the outside? It is reflex. Between 180° and 360°, and marked with an arc looping the long way round.
04 The two facts every angle question uses
Almost every angle question in a primary paper comes down to one of these. Both are about angles that share a point.
Angles on a straight line add up to 180°. If two or more angles sit side by side along a straight line, whatever they are, they total 180°.
Angles at a point add up to 360°. Angles going all the way round a point make a full turn.
So the move in nearly every question is the same: find the angles you were given, decide whether they sit on a line or round a point, and subtract from 180° or 360°.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- anglesayANG-guhlmore than oneangles
The amount of turn between two lines meeting at a point, measured in degrees. Not a length — the arms can be any length at all.
- degree, written °saydi-GREEmore than onedegrees
The unit an angle is measured in. A full turn is 360 degrees, written 360°.
- acutesayuh-KYOOT
An angle smaller than a right angle: more than 0° and less than 90°. A sharp corner.
- right anglesayRITE ANG-guhlmore than oneright angles
Exactly 90°, a quarter turn. Marked with a small square rather than a number. The corner of a page is one.
- obtusesayuhb-TYOOSS
An angle bigger than a right angle but less than a straight line: more than 90° and less than 180°.
- straight anglesaySTRAYT ANG-guhlmore than onestraight angles
Exactly 180°, a half turn. The two arms lie in a straight line.
- reflexsayREE-fleks
An angle bigger than a straight line: more than 180° and less than 360°. It is the outside of a smaller angle, and the two together make 360°.
- protractorsaypruh-TRAK-tuhmore than oneprotractors
The half-circle tool for measuring angles. Line its centre on the point and its zero line along one arm, then read where the other arm crosses.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P3
Recognising angles, comparing them to a right angle, and naming acute and obtuse.
Practise P3 Angles — 10 questions →49% of P3 papers
- P4
Measuring and drawing with a protractor, and angles on a straight line and at a point.
Practise P4 Angles — 10 questions →71% of P4 papers
- P5
Angles inside shapes, and finding an unknown angle from the ones given.
Practise P5 Angles — 10 questions →20% of P5 papers
- P6
Several steps at once — an unknown angle reached through two or three others in a composite figure.
Practise P6 Angles — 10 questions →38% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“The one with the longer arms is the bigger angle.”
Arm length has nothing to do with it. An angle measures turn, and the same turn drawn with short arms and long arms is the same angle.
“90° is acute because 90 is a small number.”
90° is exactly a right angle, and acute means less than 90°. The boundaries belong to right and straight, not to acute and obtuse.
“A reflex angle is just a big obtuse angle.”
Obtuse stops at 180°. Past a straight line the angle becomes reflex, and it is measured round the outside.
“Angles at a point add up to 180°.”
That is angles on a straight line. All the way round a point is a full turn, 360°. Choosing the wrong one of these two is the commonest way to lose the mark.
“I read 130° off the protractor, so the answer is 130°.”
A protractor has two scales, one running each way. An angle that is clearly smaller than a square corner cannot be 130°, so read the other scale: it is 50°.
Now try it
40 questions across 4 levels, marked as you go with the working shown.