Missing angles: what children learn
Year 6 pupils find unknown angles in any triangles, quadrilaterals and regular polygons, and recognise angles where they meet at a point, are on a straight line, or are vertically opposite.
In this game children use these facts to find missing angles. Each question needs the right total, 180° for a triangle or 360° for a quadrilateral, and careful subtraction.
This topic covers the Year 6 statutory requirement in the National Curriculum in England (Geometry – properties of shapes): pupils should be taught to “find unknown angles in any triangles, quadrilaterals, and regular polygons”. Year 6 pupils are usually aged 10–11.
For families following US standards, the closest Common Core standard is 8.G.A.5, which is taught in Grade 8. Angle sum of a triangle is Grade 8 in Common Core.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 180-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- Triangle: 180°. The three angles in any triangle add up to 180°.
- Quadrilateral: 360°. The four angles in any quadrilateral add up to 360°.
- Vertically opposite angles are equal. Where two straight lines cross, opposite angles are the same size.
- Regular polygons. Split the polygon into triangles from one corner. A shape with n sides has n − 2 triangles.
Worked examples
Example 1: A triangle has angles of 60° and 70°. What is the third angle?
Working: 180 − 60 − 70 = 50.
Answer: 50°
Example 2: A quadrilateral has angles of 90°, 90° and 110°. What is the fourth angle?
Working: 90 + 90 + 110 = 290. 360 − 290 = 70.
Answer: 70°
Example 3: What is each angle in a regular hexagon?
Working: A hexagon splits into 4 triangles: 4 × 180 = 720. 720 ÷ 6 = 120.
Answer: 120°
Common mistakes and how to fix them
- Using 360° for a triangle. Tear the corners off a paper triangle and put them on a straight line: 180°.
- Thinking vertically opposite angles add up to 180°. Angles next to each other on a line add to 180°. Opposite angles are equal.
- Dividing the total by the number of sides for irregular shapes. Only regular polygons have equal angles.
Activities to try at home
- Draw a triangle, measure two angles and predict the third before measuring it.
- Look for crossing lines in road markings and spot equal opposite angles.
- Find regular polygons in tiles and nuts and bolts.
Ideas for the classroom
- Pupils prove that a quadrilateral's angles add to 360° by splitting it into two triangles.
- Give multi-step angle puzzles that use two facts.
- Pupils make a table of interior angle totals for polygons with 3 to 8 sides.
Free printable game and worksheet
The free printable starts with a game sheet, such as a colour-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
Are diagrams drawn accurately?
Often not. Children should calculate using angle facts rather than measure.
What is a regular polygon?
A shape with all sides equal and all angles equal, such as an equilateral triangle or a square.
Can it be played with a keyboard?
Yes. Press 1, 2, 3 or 4 to choose an answer.