What you'll learn
This topic covers basic angle facts: angles at a point, angles on a straight line, and angles formed when a transversal crosses parallel lines. In this guide you will learn the key angle rules, how to identify equal and supplementary angles in parallel-line diagrams, how to set out reasons, and how to combine the rules to find missing angles. These facts underpin all of geometry.
Key terms and definitions
Angles at a point — angles around a point that add up to 360°.
Angles on a straight line — angles on one side of a line that add up to 180°.
Vertically opposite angles — equal angles formed when two lines cross.
Transversal — a line crossing two or more other lines.
Parallel lines — lines that never meet, marked with arrows.
Core concepts
Angles at a point and on a line
Angles at a point add up to 360°, and angles on a straight line add up to 180°. These let you find a missing angle by subtracting the known ones. When two lines cross, vertically opposite angles are equal.
Corresponding angles
When a transversal crosses parallel lines, corresponding angles are equal — they sit in the same position at each intersection, forming an "F" shape. Spotting the F shape helps you mark equal angles.
Alternate angles
Alternate angles are equal — they sit on opposite sides of the transversal between the parallel lines, forming a "Z" shape. These are a common way to find an unknown angle.
Co-interior (allied) angles
Co-interior angles add up to 180° — they sit on the same side of the transversal between the parallel lines, forming a "C" or "U" shape. They are supplementary, not equal.
Giving reasons and combining rules
In exam answers you must state the reason for each step, quoting the rule (e.g. "alternate angles are equal", "angles on a straight line sum to 180°"). Often you combine several rules with the triangle angle sum to reach the answer, working step by step.
Worked examples
Example 1: On a straight line
Two angles on a straight line are x and 110°. Find x.
180 − 110 = 70° (angles on a line sum to 180°).
Example 2: Alternate angles
A transversal crosses parallel lines; one alternate angle is 65°. Find the other.
65° — alternate angles are equal.
Example 3: Co-interior
Two co-interior angles are y and 120°. Find y.
180 − 120 = 60° (co-interior angles sum to 180°).
Common mistakes and how to avoid them
Confusing the angle pairs. Corresponding (F) and alternate (Z) are equal; co-interior (C) sum to 180°.
Assuming lines are parallel. Only use parallel-line rules if arrows show parallel lines.
Forgetting reasons. Quote the rule for every step.
Mixing 180° and 360°. A point is 360°; a straight line is 180°.
Stopping too soon. Combine rules to reach the required angle.
Exam technique for Angles
Use the basic sums — 360° at a point, 180° on a line.
Spot F, Z and C shapes for corresponding, alternate and co-interior angles.
State a reason for every step.
Combine rules with the triangle angle sum.
Check that your angles are consistent.
Quick revision summary
The basic facts are: angles at a point sum to 360°, angles on a straight line sum to 180°, and vertically opposite angles are equal. When a transversal crosses parallel lines, corresponding angles are equal (the "F" shape), alternate angles are equal (the "Z" shape), and co-interior angles sum to 180° (the "C" shape). Use parallel-line rules only when arrows show the lines are parallel. To find a missing angle, identify the right rule from the diagram, often combining several rules with the triangle angle sum, and state a reason for every step — marks are awarded for reasoning. The common errors are confusing the angle pairs, assuming lines are parallel without arrows, omitting reasons, and mixing up 180° and 360°. Learn the basic sums, spot the F, Z and C shapes, justify each step, and combine the rules to reach the answer.