GCSE Maths revision · Geometry and measures

Angles and parallel lines

Foundation and Higher

The idea

Angles on a straight line add to $180^\circ$ and angles around a point add to $360^\circ$ . Where a line crosses two parallel lines, alternate angles are equal, corresponding angles are equal and co-interior angles add to $180^\circ$ .

Find any angle you can, one step at a time.
Write the reason next to each angle.
Use the full names: alternate angles are equal, not just Z-angles.

Watch out Write the reason next to each angle: the reasons carry marks of their own.

See it worked

Worked exampleNon-calculator3 marks

Three angles meet on a straight line. Two of them are $47^\circ$ and $68^\circ$ . The third angle is $x$ .

(a) Work out the size of angle $x$ .

(b) Give a reason for your answer.

(a) Angles on a straight line add up to $180^\circ$ .
$x = 180 - 47 - 68 = 65$
(b) The three angles together make a straight line, so their sum is $180^\circ$ .

Answer (a) $65^\circ$ ; (b) Angles on a straight line add up to $180^\circ$ .

Your turn

Question 1Non-calculator2 marks

The diagram shows three angles on a straight line.

Work out the value of $x$ .

Question 2Non-calculator4 marks

$AB$ is parallel to $CD$ .

(a) Work out the value of $x$ .

(b) Work out the size of the smaller of the two angles.

Question 3Non-calculator4 marks

The diagram shows a straight line $EF$ crossing the lines $AB$ and $CD$ at $G$ and $H$ .

Is $AB$ parallel to $CD$ ? You must show how you get your answer.

In past papers

127 official questions in 106 papers since 2017. The latest:

All GCSE Maths past papers

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