Exterior angles of any polygon sum to 360°
So for a regular polygon, exterior angle and interior angle exterior. Interior-angle sum .
Three parallel-line angle facts
Corresponding angles are equal (F-shape), alternate angles are equal (Z-shape), and co-interior (supplementary) angles add to 180° (C-shape). Also: angles on a line sum to 180°, angles at a point to 360°, vertically opposite angles are equal.
Drawn from real examiner reports.
Line 180° vs point 360°
Angles on a straight line add to ; angles round a point add to . Subtracting from the wrong total is common — check whether the angles sit on a line or fill a whole turn.
Mixing up interior and exterior angles
Students confuse the two and divide when they meant the interior, or vice versa. Decide which the question wants first, then check interior exterior at a vertex.
Getting interior and exterior angles mixed up was a common mistake in examiner reports.
Not spotting an isosceles triangle
After finding one angle, students fail to notice two equal sides/angles (e.g. two radii, or a symmetric shape) that unlock the next step. Equal sides give equal base angles.
In one reported question many reached an angle of 132° but stalled because they did not see the triangle was isosceles.
Mislabelling angles on the diagram
Assigning a value to the wrong angle (e.g. deciding an interior angle is the exterior one) loses every mark even when the method is right. Label each angle on the figure before calculating.
Students who labelled their diagram incorrectly lost all their marks in examiner reports.
Alternate vs co-interior mix-up
Z-shape (alternate) angles are EQUAL; C-shape (co-interior) angles ADD to . Making co-interior angles equal, or alternate angles supplementary, is a frequent slip — name the letter shape first.
Vertically opposite angles are equal
Where two straight lines cross, vertically opposite angles are EQUAL. Students sometimes treat them as supplementary (adding to ) — that is the adjacent pair, not the opposite pair.
Label each angle with its reason
Marking angles on the figure and naming the rule earns method marks and prevents mislabelling.
Name the letter shape (F, Z, C)
On parallel lines quote the shape: F is corresponding (equal), Z is alternate (equal), C is co-interior (add to ). Naming the correct rule earns the reason mark.
Chase angles one step at a time
Find one angle at a time, writing each on the diagram with its reason, until you reach the target. Multi-step chases fall apart if you jump straight to the answer.
Give a reason for every step
Cambridge credits the geometric REASON, not just the number. Quote "alternate angles", "angles on a straight line", "angle sum of a triangle ". A value with no reason can drop the final mark.
Also basics: angles on a straight line sum to , angles at a point sum to , vertically opposite angles are equal.
Co-interior (supplementary) angles — what do they do?
Two straight lines are parallel. A transversal crosses them, and one pair of co-interior (supplementary) angles is marked. One of them is . Find the other.
