Maths topic

angles

Angles measure the amount of turn between two arms that meet at a point.

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the big idea

An angle is about turn. When two arms meet at a vertex, the size of the opening tells us the size of the angle.

turn how far one arm opens
vertex where the arms meet
degrees the unit for angle size

change the angle

Choose an angle size and watch the opening change.

90°

90°

right angle

A right angle is exactly 90 degrees.

parts of an angle

An angle has two arms and one vertex. The angle is the turn or opening between the arms.

  • The arms are the two straight lines that make the angle.
  • The vertex is the point where the arms meet.
  • The opening between the arms is the angle.
angle arm arm vertex turn

angle types

We can name angles by comparing them to a right angle and a straight line.

  • An acute angle is smaller than a right angle.
  • A right angle is exactly 90 degrees.
  • An obtuse angle is bigger than 90 degrees but smaller than 180 degrees.
  • A straight angle makes a straight line and is 180 degrees.
acute acute less than 90°
right right 90°
obtuse obtuse between 90° and 180°
straight straight 180°

arm length does not matter

Longer arms do not make a bigger angle. The angle size is the amount of turn between the arms.

  • Look at the opening, not how long the arms are.
  • Two angles can be the same size even when one drawing has longer arms.
  • If the turn is the same, the angle is the same.
55° short arms
55° long arms

Same opening, same angle.

comparing angles

To compare angles, compare how much turn or opening each angle has.

  • A smaller opening means a smaller angle.
  • A wider opening means a larger angle.
  • Two angles are equal if their openings match.
smaller smaller
right angle right angle
larger larger

right angles are special

A right angle is a square corner. It is exactly 90 degrees and is often marked with a little square.

  • Right angles are useful because they make square corners.
  • Look for right angles in paper corners, door frames, tables and grid squares.
  • A right angle is neither acute nor obtuse.
90°
paper corner door frame grid square

measuring in degrees

Angles are measured in degrees. The degree symbol is written like this: °.

  • A right angle is 90°.
  • A straight angle is 180°.
  • A full turn is 360°.
0°90°180°
90° right 180° straight 360° full turn

tools for measuring angles

A protractor helps measure angles in degrees. Digital angle tools can help you explore how the arms move.

  • Place the centre of the protractor on the vertex.
  • Line up one arm with 0°.
  • Read where the other arm points.
  • Use a known right angle to check whether an angle is smaller, equal or larger than 90°.
0°90°180°
protractor measure degrees
right angle checker compare to 90°
angle tool move the arms
clock hands see turns

measuring angles

Degrees tell us how much turn an angle has. The short symbol for degrees is °.

1 degree °

unit for angle size

2 acute < 90°

smaller than a right angle

3 right 90°

a square corner

4 obtuse > 90°

larger than a right angle but less than 180°

5 straight 180°

a straight line

6 full turn 360°

one complete turn

angle facts

right angle 90°
straight angle 180°
full turn 360°
acute angle less than 90°
obtuse angle between 90° and 180°

real world examples

doors how far a door opens
corners square corners on books, paper and tables
clocks the turn between clock hands
robots turning a robot or sprite
ramps checking steepness
sport turns in dance, skateboarding and ball games

quick angle quiz

Try a few angle ideas. This quiz only asks about ideas shown on this page.

What part of an angle is the point where the arms meet?

Does making the arms longer make the angle bigger?

How many degrees are in a right angle?

What do we use to measure angles?