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SavannahYear 8
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MathsNumber, algebra and geometry: connected foundations30 min★★ difficulty

Chapter 7: Angle facts and parallel lines

Angle diagrams are chains of reasons: each value should follow from a named fact.

Part of your national curriculum
  • Geometry and measures: Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines

Lesson overview

What you'll learn in this lesson

Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines

Key learning points

  • • Core facts
  • • Parallel lines
  • • Write the reason

This lesson at a glance

  • 30 minutes
  • 14 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

propertiesanglesstraightverticallyopposite

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Chapter 7: Angle facts and parallel lines

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Core facts

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 14

Learn

Core facts

Angles on a straight line total 180°, around a point total 360°, and vertically opposite angles are equal.

4

Explore the idea

Part 4 of 14

Learn

Parallel lines

When a transversal crosses parallel lines, corresponding and alternate angles are equal; co-interior angles total 180°. Arrow markings are essential evidence that lines are parallel.

5

Quick check

Part 5 of 14

Quick check

Angles on a straight line total:

6

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 14

Quick check

Vertically opposite angles are:

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Write the reason

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 14

Learn

Write the reason

Do not merely calculate. State, for example, x = 68° because alternate angles between parallel lines are equal.

10

Quick check

Part 10 of 14

Quick check

Co-interior angles between parallel lines total:

11

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

____ on a straight line total 180°, around a point total 360°, and vertically opposite angles are equal.

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Chapter 7: Angle facts and parallel lines

3 questions, marked with the reasoning shown. No timer.

  1. 1. Angles on a straight line total:

  2. 2. Vertically opposite angles are:

  3. 3. Co-interior angles between parallel lines total:

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

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Games

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Points this lesson

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Best run

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Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

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Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 14 · Watch & discover

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    Apply the properties of angles at a point, on a straight line, vertically opposite angles, and angles in parallel lines

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