Angles in Parallel Lines (Cambridge International IGCSE Mathematics)

Angles in parallel lines

What are parallel lines?

• Parallel lines are lines that are always equidistant(the same distance apart)

  • No matter how far the lines are extended in either direction, they will never meet

• Angles are formed when a straight line cuts through two parallel lines

What are corresponding angles in parallel lines?

• Find corresponding angles by looking for an F-shape
• Corresponding angles are equal

Corresponding angles

What are alternate angles in parallel lines?

• Find alternate angles by looking for a Z-shape
• Alternate angles are equal

Alternate angles

What are co-interior (supplementary) angles in parallel lines?

• Find co-interior angles by looking for a C-shape
• Co-interior angles add up to 180°

Co-interior angles

How do I find missing angles in parallel lines?

• Look for shapes that look like F, Z, or C

• Vertically opposite angles can also be used in problems involving parallel lines

  • The below diagram shows how identifying angle x, can lead to knowing information about several other angles

    • The green angle opposite is also x, as it is vertically opposite
    • The orange angle must be 180-x as angles on a straight line sum to 180°

• You should also be able to spot corresponding angles, alternate angles, and co-interior angles in this diagram

Exam Hint Do not forget to give reasons for each step of your working in an angles question. These are often needed to get full marks

You must use the correct names as listed above. Do not use F, Z and C angles otherwise you will lose marks!

Worked Example Find the size of the angles a and b in the diagram below.

Give a reason for each step in your working.

Answer:

Final answer: a = 64° (Vertically opposite angles are equal)** b = 64° (Corresponding angles on parallel lines are equal)**