Compare and order angles

Part of MathsLines and anglesYear 5

What is an angle?

An angle is the space between two lines that start at the same point. This point is called the vertex.

Angles measure the size of a turn in degrees. You can show degrees using the symbol ° after the number of degrees.

Two straight lines meet at a point called the 'vertex point'. The angle is marked between two lines. Opposite the angle and the vertex point, a curved arrow goes from one end of one of the lines to the other. and is labelled 'turn.'

Imagine two lines acting like the hands of a clock. When the hands move apart, the space between them gets bigger or smaller - that space is the angle.

Angles can be seen everywhere - in shapes, opening doors, and even when you stretch your arms. Knowing about angles can help you understand how things fit and move together.

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Quiz: Comparing angles

Test out your knowledge of comparing and ordering angles with this quiz, then read on to complete the page.

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Types of angles

There are many different types of angles. An angle’s type can depend on the size of the turn and how wide the angle is.

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  1. Left is a right angle formed by two lines, with a small square in the corner. On the right is a book, with a square in the bottom-right corner.

    Right angle

    A right angle is 90° or a quarter turn. It looks like the corner of a square or rectangle. You can spot right angles in doors, books or the edge of a piece of paper.

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How to measure angles

You can use a tool called a protractor to measure angles accurately.

An image of a protractor, a semi circle with angle measurements. On the left the angle starts at 0° increasing to 180° in increments of 10 as it gets to the other side of the protractor

Protractors can measure angles of different sizes, such as right, acute, and obtuse angles.

Follow these steps to measure an angle using a protactor:

  1. Place the centre point of the protractor on the angle’s vertex - the point where two lines meet.
  2. Line up one side of the angle with the zero line on the protractor.
  3. Read the degree mark where the other side crosses the protractor.

The protractor in the image below has been used to measure an angle of 110°.

A protracator measuring an angle which reads 110°. An arch shows the turn between 0° and 110°.
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Example 1

An acute angle is less than 90°, a right angle is exactly 90°, and an obtuse angle is between 90° and 180°.

A grid of six labelled angles. Angle a is 70°, Angle b is 90°, Angle c is 90°, Angle d is 120°, Angle e is 150° and Angle f is 25°

Which of the angles shown are acute and which are obtuse?

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Example 2

Remember that:

  • an acute angle looks small and sharp
  • an obtuse angle appears wide and open
  • a reflex angle is larger than a straight line
A grid of six unlabelled angles. Angle a is smaller than 90°,, Angle b is larger than 90° but smaller than 180°, Angle c is larger than 180°, Angle d is smaller than 90°, Angle e is larger than 180° and Angle f is larger than 90° but smaller than 180°.

Which of the angles shown are acute, which are obtuse and which are reflex?

See if you can answer without using a protractor.

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Example 3

The greater than and less than signs can be used to describe comparisons between angles.

A grid of three unlabelled angles. Angle a is larger than 90°, Angle b is smaller than 90°, and Angle c has a square marker.

Put these three angles in the correct order from smallest to largest.

Use the less than sign in your answer.

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