IGCSE Mathematics (0580)

Angles

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

The exterior angle of a triangle at a vertex equals the sum of the two non-adjacent interior angles, not just the adjacent angle or the triangle's total.
Common mistake: Students often mistakenly subtract from 180° or add the wrong angles.
Angles on a straight line sum to 180°, so to find a missing angle when several adjacent angles are given, add the known angles and subtract from 180°.
Common mistake: Students often forget to include all given angles or use 360° instead.
The sum of the three angles in any triangle is 180°, so when one angle is a right angle (90°), subtract both the right angle and the given angle from 180° to find the missing angle.
Common mistake: A common mistake is to forget to subtract the right angle.
In an isosceles triangle, the two equal angles are opposite the equal sides, so to find the third angle, add the two equal angles and subtract from 180°.
Common mistake: A common mistake is not identifying which angles are equal.
Bearings are measured clockwise from North at the starting point, so to find the bearing of A from C.
Common mistake: Students must visualize or sketch the positions and measure from C, not confuse it with the reverse bearing from A.
To find the number of sides in a regular polygon, divide 360 by the EXTERIOR angle (180 minus the interior angle).
Common mistake: A common mistake is dividing 360 by the interior angle directly.

Find the value of z.

Try it first, then show the working

The exterior angle of a triangle equals the sum of the two opposite interior angles.
z = 47 + 68 = 115.
Check: angle PRQ = 180 - 47 - 68 = 65, and 180 - 65 = 115.

Answer: z = 115

24 exam-style questions on Angles, each marked to the scheme.