Angle rules and properties of shape
Maths · Key Stage 3 · The School
The facts you build everything from
Angles on a straight line add to 180°. Angles round a point add to 360°. Angles in a triangle add to 180°; in a quadrilateral, 360°. Vertically opposite angles are equal. Five facts — every angle question in the curriculum is these five, used in some order.
Parallel lines: F, Z and C
Where a line crosses two parallels: corresponding angles are equal (the F shape), alternate angles are equal (the Z shape), and co-interior angles add to 180° (the C or U shape). Trace the shape with your finger on the diagram before writing anything — spotting the letter is what identifies the rule.
Polygons and the reason column
Exterior angles of ANY polygon add to 360°, so each exterior angle of a regular n-gon is 360/n and each interior angle is 180 − 360/n. In an exam you get marks for the REASON, not just the number: "angles on a straight line sum to 180°". Write the reason every time you write a number, and the method mark is yours even if the arithmetic slips.
Two parallel lines are crossed by a straight line. The angle at the top is 62°. Find x, the angle marked at the bottom on the other side. Step 1: the angle vertically opposite 62° is 62° (vertically opposite angles are equal). Step 2: that angle and x are alternate (the Z shape), so x = 62° (alternate angles are equal). Two lines of working, two reasons — and in an exam the reasons are worth as much as the number.