Mathematics

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50 mins

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+80 XP

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IWB/Projector/Large Screen

Angle Sum of a Quadrilateral

Discover why any quadrilateral's four angles always add up to 360° by splitting it into two triangles, then use this rule to find missing angles in four-sided shapes.

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1 Getting Started
2 Watch and Notice
3 Split and Show It in Your Copy
4 Try It Together
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Picture a four-sided shape with one line ruled from a corner straight across to the opposite corner. That one line splits the shape into two triangles.

Key point

You already know that the three angles inside a triangle add up to 180°. So have a go at this before we work it out: if a quadrilateral is made of two triangles, what do you think all four of its angles add up to?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Here are three quadrilaterals side by side. Each one already has its four angles labelled and its total printed underneath. Read the printed total on each shape and notice what they all have in common.

Whatever the shape, the four angles land on the same total. Once each triangle is worth 180° and one diagonal makes two triangles, that total is 2 × 180° = 360°. Every quadrilateral's four angles add up to 360°.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Split and Show It in Your Copy ~4 mins

COPYBOOK MOMENT

In your maths copy, draw a quadrilateral of your own. Rule one diagonal from a corner to the opposite corner to split it into two triangles.

Write 180° inside each triangle, then show underneath how they combine:

Triangle 1 = 180°
Triangle 2 = 180°
2 × 180° = 360°

+10 XP

4 - Try It Together ~9 mins

Today we work through a quadrilateral together on the board by dragging its corners.

Key point

One pupil drags a corner and the four angles change on screen. Everyone else watches the shape and predicts which angle will shrink before the drag — and checks together that no matter how the shape bends, the four angles still add to exactly 360°.

Bend the quadrilateral, watch the sum

+15 XP

5 - Class Challenge ~8 mins

Today we find the missing angle in each of these quadrilaterals in turn. Three angles are given and we work out the fourth so the four add to 360°:

90°, 90°, 90° → find the fourth
100°, 80°, 100° → find the fourth
120°, 60°, 100° → find the fourth
85°, 95°, 130° → find the fourth

How to work

Work each one out quietly in your head first, then we check it together on the board. You are not expected to get it right first time — the last ones are trickier on purpose, and trying the method even when you are unsure is exactly what we are practising.

Find the missing angle

+15 XP

Pupil practice

Module 7 · 2D Shape, 3D Shape and Angles Shape & Space

Lesson 82 · Angle Sum of a Quadrilateral

Download Activity Book page (PDF)

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