Use angle facts at a point and on a line, in triangles and quadrilaterals, the corresponding, alternate and co-interior angles in parallel lines, and the interior and exterior angle properties of polygons, giving reasons.

What this dot point is asking

This is the foundation of WJEC geometry. You are asked to find unknown angles using the basic angle facts (angles at a point, angles on a straight line, vertically opposite angles), the angle sums of triangles and quadrilaterals, the parallel line rules (corresponding, alternate and co-interior angles), and the interior and exterior angle properties of polygons. The skill that earns full marks is not just the arithmetic but giving the correct reason at each step, because WJEC examines geometric reasoning under AO2 and AO3. It appears on both components and at every tier.

Basic angle facts

A handful of facts let you find most missing angles.

So if three angles meet at a point and two are $130^\circ$ and $95^\circ$, the third is $360^\circ - 130^\circ - 95^\circ = 135^\circ$. These facts are the building blocks, and each step in a worded answer needs the relevant fact named.

Angles in triangles and quadrilaterals

The angle sums of the basic shapes follow from the straight-line fact.

The three angles of any triangle sum to $180^\circ$, and the four angles of any quadrilateral sum to $360^\circ$. Special triangles help: an isosceles triangle has two equal angles (the base angles), an equilateral triangle has three $60^\circ$ angles, and a right-angled triangle has one $90^\circ$ angle leaving the other two to sum to $90^\circ$. The exterior angle of a triangle equals the sum of the two interior opposite angles, a useful shortcut that WJEC questions reward.

Angles in parallel lines

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

The informal F, Z and C shapes help you spot the pairs, but in the exam you must give the formal name as the reason. Chains of these relationships, combined with the basic facts, solve multi-step parallel line problems.

Interior and exterior angles of polygons

A polygon is a closed shape with straight sides; a regular polygon has all sides and all angles equal.

So a regular hexagon ($n = 6$) has interior angles summing to $(6-2)\times 180^\circ = 720^\circ$, giving each interior angle $720^\circ \div 6 = 120^\circ$. The exterior-angle route is faster for "find the number of sides" questions: divide $360^\circ$ by the exterior angle.

Worked angle chase

A typical WJEC question chains several facts together.

Why this matters

Angle reasoning underpins the whole geometry strand. Circle theorems, polygon problems, bearings, constructions and proofs all rest on the basic facts and the parallel line rules, and WJEC routinely combines them in multi-step questions worth several marks. Because a large share of the marks rewards reasoning, the discipline of naming each fact ("alternate angles are equal", "angles on a line sum to $180^\circ$") is the highest-value habit in this topic. A correct value with no reason often scores less than full marks.