Angles in parallel lines

When a straight line crosses two parallel lines, it makes pairs of angles that are equal or add up to 180°. Look for the letters Z, F and C in the diagram.

Key facts

  • Alternate angles (Z shape) are equal.
  • Corresponding angles (F shape) are equal.
  • Co-interior angles (C shape) add up to 180°.
  • Vertically opposite angles are equal.

Worked examples

Example 1

The lines are parallel. Find x and give a reason.

  1. The 62° and x make a Z shape.
  2. Alternate angles are equal. x = 62°

Answer: x = 62°

Example 2

The lines are parallel. Find y.

  1. The 62° and y make a C shape.
  2. Co-interior angles add to 180. 180 − 62 = 118
  3. So y = 118°

Answer: y = 118°