Angles in Parallel Lines

Grade 4

What happens when a line crosses parallel lines

When a straight line (called a transversal) crosses two parallel lines, it creates a set of angles with reliable relationships. You need to recognise three types.

Alternate angles are equal — they sit on opposite sides of the transversal in a Z-shape. Corresponding angles are equal — they sit in the same position at each parallel line in an F-shape. Co-interior angles (also called allied angles) add up to 180° — they sit on the same side of the transversal in a C-shape.

A memory trick

Z = alternate (equal). F = corresponding (equal). C = co-interior (supplementary, add to 180°). Draw the letter shape over the diagram to spot which type you are looking at.

Worked example

EXAMPLE

Two parallel lines are cut by a transversal. One angle formed is 115°. Find the alternate angle and the co-interior angle on the same side.

Alternate angles are equal, so the alternate angle = 115°. Co-interior angles add to 180°, so the co-interior angle = 180° − 115° = 65°.

Watch out for the direction of the arrows

Arrows on lines in diagrams mark them as parallel. If there are no arrows, you cannot assume the lines are parallel — you would need to prove it first or use a different approach.

Try this one

The diagram shows two parallel lines and a transversal. Angle p is marked.

Lines \( m \) and \( n \) are parallel. The angle at line \( m \) (below-right of the intersection) is \( 72^\circ \). Find angle \( p \) at line \( n \) (above-left of the intersection). [2]

Nova's hint:

This involves alternate angles formed by a transversal crossing two parallel lines.

Ask yourself: 'Are these angles on opposite sides of the transversal, between the parallel lines?' If two angles form a 'Z' or 'N' shape, what is the relationship between them?

Try to Solve it with Nova?