Alternate Angles (Z)

Alternate angles are equal. They form a Z shape between parallel lines.

Formula: Alternate angles are equal

Example: Angle = 65° → Alternate = 65°

Corresponding Angles (F)

Corresponding angles are equal. They form an F shape.

Formula: Corresponding angles are equal

Example: Angle = 110° → Corresponding = 110°

Co-interior Angles (C)

Co-interior (allied) angles add up to 180°. They form a C or U shape.

Formula: Co-interior add to 180°

Example: Angle = 70° → Co-interior = 110°

Vertically Opposite

Angles opposite each other when two lines cross are ALWAYS equal.

Angles on a Point

Angles around a point add up to 360°.

Multi-Step Problems

Combine angle rules: use alternate, corresponding, vertically opposite, and angles on a line together.

Example: If angle a = 55° (alternate) Angle b = 180° − 55° = 125° (straight line)

Proofs

You may be asked to prove that lines are parallel by showing that alternate or corresponding angles are equal.

Geometric Reasonings

In Higher tier, you often need to provide a chain of reasons for every step in an angle calculation.

Parallel Lines in Shapes

Parallel lines properties often appear inside parallelograms, rhombuses and trapezia.