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How to calculate an angle

You can use pattern-spotting, logic and reasoning to work out angles around straight lines.

Some facts that are useful to remember are:

  • 360° is a full turn
  • 180° is half a turn
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Angles on a straight line

Did you know that one half turn is 180°?

If the straight line or half turn is divided into two angles, and we know one of the angles, we can work out the other.

Here 120° + 60° = 180°

An 180° angle divided into two angles: 120° and 60°

If we just had information on one of the angles e.g. 120°, we could work out the other angle is 60°.

If the straight line was divided into three angles, all three angles would add up to 180°.

Here are some more examples of angles on straight lines, can you see how they all add up to 180°?

Different angles on a straight line adding up to 180°. 50° and 130°, 20° and 160°, 115° + 65°, 146° + 34°
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Example 1

vertically opposite angles

Can you work out what angle b is?

b is on a straight line with 140°, so must be 40°.

140° + 40°= 180°

What about angle c?

b + c = 180°, so if b is 40°, c must be 140°.

40° + 140° = 180°

Angle d must be 40° as it is on a straight line with c.

c+ d = 180°

vertically opposite angles
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Vertically opposite angles

Vertically opposite angles are the angles directly opposite each other when a straight line crosses over another straight line.

They are always equal.

What do you think angle c is in both of these diagrams?

vertically opposite angles

In the first diagram angle c equals 70° and in the second diagram angle c equals 145°.

Angles b and d are vertically opposite, so they are equal too.

Remember

Remember

  • Angles on a straight line add up to 180°.
  • When two straight lines cross, vertically opposite angles are always equal.
Remember
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Activities

Quiz 1

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Quiz 2

Take this quiz to practise solving problems with angles.

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NEW! Play Guardians: Defenders of Mathematica - the Halloween update
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More on Lines and angles

Find out more by working through a topic