KS2 Mathematics: Missing Angles in Shapes and at Points

Finding a missing angle is one of the most common geometry tasks on the reasoning papers of the Key Stage 2 mathematics tests. The Year 6 national curriculum asks pupils to find unknown angles in any triangle, quadrilateral and regular polygon, and to recognise angles where they meet at a point, are on a straight line, or are vertically opposite. The skill is not measuring with a protractor but reasoning: knowing which fact applies and explaining it.

This material trains that reasoning: every angle is given in words, and most problems also come with a diagram, as on the test. The twelve quiz questions cover angles around a point, three angles on a straight line, the angle vertically opposite a given angle and the angle next to it where two lines cross, the third angle of a scalene triangle, both kinds of isosceles triangle problem (given the top angle, and given a base angle), the angles of an equilateral triangle, the fourth angle of a quadrilateral, the angles of a parallelogram, and the interior angles of a regular hexagon and a regular octagon, found by splitting the shape into triangles. The wrong options are the usual confusions: using 180° where 360° is needed, mixing up vertically opposite and neighbouring angles, and forgetting that an isosceles triangle has two equal base angles.

The flashcards hold the facts you need: angles on a straight line, around a point, vertically opposite angles, the angle sums of triangles and quadrilaterals, the properties of isosceles and equilateral triangles, how to find the angle sum of any polygon by splitting it into triangles, how to find one angle of a regular polygon, and the words acute, obtuse and reflex.

The printable written work has eight problems that ask for reasons as well as answers: the four angles where two lines cross, equal angles around a point, angles on a straight line, an isosceles triangle with an obtuse angle, a kite, a regular pentagon, a triangle with one side extended, and a question about which regular shapes can fit together around a point without gaps. Writing the reason next to each step, for example 'angles on a straight line add up to 180°', is exactly the habit the reasoning papers reward.

In the oral exam an examiner describes an angle problem, asks for the missing angle and then asks which angle fact you used.

The material is aimed at Year 6 pupils preparing for the end of Key Stage 2 tests. Sketching each problem quickly on paper, even roughly, makes it much easier to see which angles are equal and which add up to 180° or 360°.

• Find missing angles on a straight line, around a point and where two lines cross
• Recognise that vertically opposite angles are equal
• Find unknown angles in scalene, isosceles and equilateral triangles
• Find unknown angles in quadrilaterals, including parallelograms and kites
• Find the angle sum and each interior angle of regular polygons by splitting them into triangles
• Explain each step with the correct angle fact

Practice material written by Zestly, based on the Year 6 mathematics programme of study in the national curriculum for England (DfE, 2013): geometry, properties of shapes (unknown angles in triangles, quadrilaterals and regular polygons; angles at a point, on a straight line and vertically opposite).