Angles in parallel lines · Year 9

In Year 9 you learn: multi-step angle problems.

When a straight line (a transversal) crosses two parallel lines, it makes the same angles at each crossing. Corresponding, alternate and co-interior angles let you move angles from one crossing to the other.

Key facts

  • Corresponding angles (F shape) are equal.
  • Alternate angles (Z shape) are equal.
  • Co-interior angles (C shape) add up to 180°.
  • At each crossing, vertically opposite angles are equal and neighbouring angles add to 180°.
  • Arrows on lines show that they are parallel.

Worked examples

Example 1

The two lines are parallel. Find the angle x.

Answer: x = 62°

Example 2

A line crosses two parallel lines. One of the angles between them is 112°. Find x.

Answer: x = 68°

Example 3

The lines are parallel. The marked angles are (3x + 15)° and (5x − 25)°. Find x and the size of the angles.

Answer: x = 20; both angles are 75°

Example 4

The two horizontal lines are parallel. Find the angle x at the bend.

Answer: x = 75°

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