Use angle facts at a point, on a straight line and in parallel lines (alternate, corresponding and co-interior); and calculate the interior and exterior angles of polygons.

What this dot point is asking

The Eduqas geometry content requires you to use the basic angle facts (angles at a point, on a straight line, vertically opposite, and the angles formed when a transversal crosses parallel lines) and to calculate the interior and exterior angles of polygons. Angle reasoning is the foundation of geometry, and Eduqas tests it through "find the angle, giving reasons" questions where the reasoning is worth marks in its own right. It appears at both tiers, with polygon-angle and parallel-line problems being reliable mid-tariff questions, and the requirement to justify each step makes it an AO2 communication test.

Basic angle facts

A handful of facts underpin all angle work, and Eduqas expects you to name the one you use.

So if three angles meet at a point and two are $130^\circ$ and $90^\circ$, the third is $360^\circ - 130^\circ - 90^\circ = 140^\circ$. The skill is choosing the right fact for the configuration and stating it, because "giving reasons" questions award a mark for the justification as well as the value.

Angles in parallel lines

When a straight line (a transversal) crosses two parallel lines, three angle relationships appear.

Recognising the shape points to the rule: an F-shape means equal corresponding angles, a Z-shape means equal alternate angles, and a C-shape means co-interior angles adding to $180^\circ$. Many exam diagrams combine several steps, so work across the figure one named relationship at a time.

Interior and exterior angles of polygons

A polygon's angles follow two rules that work for any number of sides.

So a hexagon ($n = 6$) has interior angles summing to $(6 - 2) \times 180^\circ = 720^\circ$, and a regular hexagon has each interior angle $\dfrac{720^\circ}{6} = 120^\circ$. The exterior-angle rule is often the quicker route: to find the number of sides from a regular polygon's interior angle, find the exterior angle first, then divide $360^\circ$ by it.

Why angle reasoning matters

Angle facts are reused throughout geometry: triangle and quadrilateral proofs, circle theorems, bearings and trigonometry all rest on them. Because Eduqas weights reasoning at half the marks, the explicit "give a reason for each step" instruction means that naming the correct fact (alternate angles, angles on a straight line) is examined directly, so a fluent geometric vocabulary is as valuable as the arithmetic.