Angle Relationships
Two straight lines crossing at a point create angles that are never random — they follow two exact rules. This site explains those rules, shows how examiners use them, and lets you practise until they are automatic.
Learning outcomes
- Identify vertically opposite angles formed by two intersecting straight lines.
- Use the fact that vertically opposite angles are congruent to find unknown measures.
- Recognise accumulative angles at a point and use the 360° sum.
- Solve equations in x that come from angle relationships in a figure.
Key vocabulary
- Vertically Opposite Angles (V.O.A.)
- Two non-adjacent angles formed by the intersection of two straight lines. They are always congruent.
- Accumulative Angles at a Point
- Angles with the same vertex that completely surround the point. Their measures add up to 360°.
- Congruent angles
- Angles that have exactly the same measure in degrees.
The two rules in one line each
Rule 1 — if two straight lines intersect, each pair of vertically opposite angles is equal.
Rule 2 — the measures of all angles accumulated at a point add up to 360°.
Almost every exam question in this lesson is one of these two rules, sometimes combined with a straight angle of 180° or an angle bisector.
Lesson map
The Lesson
Definitions, rules and annotated diagrams for both angle relationships.
Worked Examples
Step-by-step model solutions plus 'Try it yourself' tasks with hidden answers.
Exercises
Completion items, find-the-value-of-x figures, multiple choice and creative thinking.
Activities & Games
Timed quiz, 360° balance challenge and an unlimited find-x generator.