Parallel and Intersecting Lines

Angles made by intersecting lines and by a transversal crossing two parallel lines: which pairs are equal and which add up to 180°.

Key ideas

When two lines cross, vertically opposite angles are equal and neighbouring angles add up to 180° (a linear pair).
Perpendicular lines meet at 90°.
A transversal crossing two parallel lines makes 8 angles of only two sizes, which add up to 180°.
With parallel lines, corresponding angles are equal and alternate angles are equal.
Co-interior angles (on the same side, between the lines) add up to 180°.
If corresponding or alternate angles are equal, the lines must be parallel.

Linear pair	a + b = 180°
Vertically opposite	a = b
Parallel lines	corresponding equal; alternate equal; co-interior add to 180°

Using the parallel-line rules when the lines are not parallel.
Making co-interior angles equal instead of adding them to 180°.
Mixing up alternate (opposite sides of the transversal) and corresponding (same position) angles.

A transversal crosses two parallel lines, making 8 angles. One of them is 122°. What are the sizes of all 8 angles?

Working: corresponding, alternate and vertically opposite angles are equal; linear pairs add to 180°

Answer: four of 122° and four of 58°