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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

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°

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°?

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 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?

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

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

Take this quiz to practise solving problems with angles.