GCSE Maths: Angles and Polygons

Angle reasoning is the backbone of GCSE geometry: nearly every geometry question on the paper either is an angle chase or contains one. This quiz assembles the complete angle toolkit for both tiers, with every configuration described fully in words and numbers so the reasoning — not diagram-reading — is what gets practised.

The set opens with the foundations: vertically opposite angles at intersecting lines, the angle sum of a triangle, and the properties of angles formed when a transversal crosses parallel lines — knowing precisely which of alternate, corresponding and co-interior angles are equal and which are supplementary, a distinction the multiple-choice format tests sharply. Quadrilateral knowledge appears through the properties of a parallelogram, separating what is always true from what only holds for rectangles.

Polygon questions form the core of the set: the interior angle sum formula (n − 2) × 180° applied to a hexagon, the fact that exterior angles of any polygon total 360°, and both directions of the regular polygon relationship — from exterior angle to number of sides (360 ÷ 40 = 9) and from side count to each interior angle of an octagon. A statement-selection question probes the interior–exterior relationship itself, including the tempting but false claims that trip students up, such as "the interior angle is always larger than the exterior angle".

Bearings close the set with the two facts the specification requires: bearings are measured clockwise from North and written with three figures, and a back bearing differs from the forward bearing by 180°. Each explanation names the theorem or rule being applied, building exactly the habit that "give a reason for your answer" questions demand on the real paper.

• Apply angle facts at a point, on a line and at intersecting lines
• Distinguish alternate, corresponding and co-interior angles in parallel lines
• Use interior and exterior angle rules for regular and irregular polygons
• Move between exterior angle, interior angle and number of sides of a regular polygon
• Work with three-figure bearings, including back bearings

Topic scope follows the Geometry and measures strand of the Department for Education's GCSE mathematics subject content: angle facts at points and on lines, angles in parallel lines, properties of triangles, quadrilaterals and polygons including interior and exterior angle sums, and bearings.