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6.2 Angles in Parallel Lines

GCSE Maths Foundation · Edexcel · Chapter 6: Angles

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: alternate, corresponding and co-interior angles, giving reasons, and angle problems with algebra. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Recognise alternate, corresponding and co-interior angles
  • Use these facts to work out missing angles
  • Give a correct reason for each step of an angle problem
  • Form and solve equations using angles in parallel lines

Key words

  • Parallel lines: Straight lines that never meet. They are marked with matching arrows.
  • Transversal: A line that crosses two or more other lines.
  • Alternate angles: On opposite sides of the transversal, between the parallel lines (a Z shape). They are equal.
  • Corresponding angles: In the same position at each crossing (an F shape). They are equal.
  • Co-interior angles: On the same side of the transversal, between the parallel lines (a C shape). They add up to 180°.

Three angle pairs

When a transversal crosses two parallel lines it makes 8 angles. Look for the letters Z, F and C hidden in the diagram.

Key fact: Alternate angles are equal. Corresponding angles are equal. Co-interior angles add up to 180°.

Finding missing angles

Worked example: one angle gives all the others

a = 180° − 115° = 65° (angles on a straight line add up to 180°)
b = 65° (corresponding angles are equal)
c = 180° − 65° = 115° (angles on a straight line add up to 180°)
Check: b and the 115° angle are co-interior: 65° + 115° = 180° ✓

Answer: a = 65°, b = 65°, c = 115°

Giving reasons

In the exam you often have to “give reasons”. Use the full, correct wording.

  • Alternate angles are equal.
  • Corresponding angles are equal.
  • Co-interior angles add up to 180°.
  • Vertically opposite angles are equal.
  • Angles on a straight line add up to 180°.
  • Angles in a triangle add up to 180°.

Writing just “Z angles” or “F angles” will not get the reason mark.

Worked example: an angle between two parallel lines

Draw a line through the corner, parallel to the other two.
The top part is 40° (alternate angles are equal). The bottom part is 35° (alternate angles are equal).

Answer: the angle at the corner = 40° + 35° = 75°

Using algebra

Worked example: alternate angles

Two alternate angles are 3x + 10° and 2x + 35°. Find the size of each angle.
Alternate angles are equal: 3x + 10 = 2x + 35, so x = 25.
Angle = 3 × 25 + 10 = 85°

Answer: 85°

Worked example: co-interior angles

Two co-interior angles are 2x and x + 30°. Find x.
Co-interior angles add up to 180°: 3x + 30 = 180, 3x = 150, x = 50.

Answer: x = 50 (angles 100° and 80°)

Key fact: You can prove lines are not parallel: if two co-interior angles do not add up to 180°, the lines are not parallel.

Common mistakes

  • Saying co-interior angles are equal. They add up to 180°.
  • Using parallel-line facts when the lines are not marked as parallel.
  • Writing “Z angles” as a reason. Write “alternate angles are equal”.
  • Mixing up which pair is which: find the Z, F or C shape before you decide.

Revision questions

Try these, then check your answers below each one.

Question 1. A transversal crosses two parallel lines. What are the angles in an F shape called? (Choose from: Corresponding angles, Alternate angles, Co-interior angles, Vertically opposite angles.)

Answer: Corresponding angles

Working: F shape: corresponding angles (equal). Z: alternate. C: co-interior.

Question 2. A transversal crosses two parallel lines. One angle is 58°. What is the size of the angle alternate to it?

Answer: 58 °

Working: Alternate angles are equal, so 58°.

Question 3. Two co-interior angles are made by a transversal crossing two parallel lines. One is 47°. Work out the other.

Answer: 133 °

Working: 180 - 47 = 133°

Related lessons

Continue in the full course

This lesson is section 6.2 (EGCMF0602) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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