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

OCR references G1 and G3 cover the angle facts at a point, on a straight line and in parallel lines, and the interior and exterior angles of polygons. Angle reasoning is the backbone of the geometry strand and a frequent "give a reason" question that tests AO2 communication directly. These facts appear on every tier and underpin circle theorems, bearings and trigonometry, so knowing them by name and using them to justify each step is essential.

Angle facts at a point and on a line

The basic angle facts come from full and half turns.

So if three angles on a straight line are $x$, $50^\circ$ and $70^\circ$, then $x = 180 - 50 - 70 = 60^\circ$. Where two straight lines cross, the angles opposite each other are equal, and adjacent angles add to $180^\circ$. OCR expects the reason ("angles on a straight line sum to $180^\circ$") alongside the working, because the reasoning earns marks in its own right.

Parallel-line angles

A transversal crossing parallel lines creates three named angle relationships.

So if a transversal makes an angle of $75^\circ$ with one parallel line, the alternate angle on the other line is also $75^\circ$, the corresponding angle is $75^\circ$, and the co-interior angle is $180 - 75 = 105^\circ$. Recognising the Z, F and C shapes in a busy diagram is the skill; once spotted, the relationship gives the angle immediately.

Interior and exterior angles of polygons

Polygon angles follow two key rules.

So a hexagon ($n = 6$) has interior angles summing to $(6 - 2) \times 180 = 720^\circ$, and a regular hexagon has each interior angle $720 \div 6 = 120^\circ$. The exterior-angle route is often quicker for regular polygons: a regular pentagon has exterior angle $360 \div 5 = 72^\circ$, so each interior angle is $180 - 72 = 108^\circ$.

Why angle reasoning matters

Angle facts are the foundation of every geometry proof and of bearings, and OCR sets multi-step "find the angle, give a reason" questions where each justified step earns a mark. Writing the reason in standard language (alternate angles, exterior angle sum, angles in a triangle) is exactly the AO2 communication the board rewards. These facts also feed directly into circle theorems, where the same straight-line and triangle rules reappear.