Mathematics

Advanced

50 mins

Teacher/Student led

Learning Goals

Learning Outcomes

Lesson Files

+80 XP

What you need:
IWB/Projector/Large Screen
Protractor

Angles on a Line, at a Point and Vertically Opposite

Learn three essential angle facts: angles on a straight line sum to 180°, angles around a point sum to 360°, and vertically opposite angles are equal. Practise spotting which fact applies and calculating missing angles.

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

1 - Getting Started ~4 mins

Illustration for Getting Started Look at the board: two straight roads cross each other, and one of the four angles is marked 70°.

What can we say about the other three angles just by looking? Which ones do you think are also 70°, and which are different?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~10 mins

Three angle facts come up on screen, one at a time: angles on a straight line, angles round a point, and two lines crossing. Watch what stays the same each time and work out each missing angle from the fact shown.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~10 mins

What to do

Today we work these out together on the board. Predict each missing angle before we check it.

A line: one angle is 140°. Find the other.
A point: 90°, 150° and one unknown. Find the unknown.
A crossing: one angle is 55°. Name all four angles.

Find the missing angle

+15 XP

4 - Sketch and Solve in Your Copy ~6 mins

COPYBOOK MOMENT

In your maths copy, sketch the three diagrams you just worked (line, point and cross). Under each one, write the calculation that finds the missing angle, for example 180° − 140° = 40°. Ring your answer.

+10 XP

5 - Class Challenge ~10 mins

Today we work through these angle problems together, each a little trickier: a road junction, a set of rays around a point, a clock-hand cross, and finally two angles on a line that are in the ratio 2:1.

Worked example

For the ratio 2:1, the bigger angle is 2 parts and the smaller angle is 1 part. That is 2 parts + 1 part = 3 equal parts altogether. The line is 180°, so one part is 180° ÷ 3.

Key point

Spot the fact you need before you calculate: 180° on a line, 360° round a point, or equal opposite angles.

Angle reasoning

+15 XP

Pupil practice

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

Lesson 80 · Angles on a Line, at a Point and Vertically Opposite

Download Activity Book page (PDF)

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