Good Learning Co.
SavannahYear 8
← Maths
MathsShape and space25 min★★ difficulty

Angle sums in triangles and polygons

Every polygon, no matter how many sides, can be sliced into triangles — and that single fact unlocks its whole angle sum.

Part of your national curriculum
  • Geometry and measures: Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

Lesson overview

What you'll learn in this lesson

Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

Key learning points

  • • Triangles first
  • • Worked example: polygon sum
  • • Worked example: missing angle

This lesson at a glance

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

Words to know

deriveanglestrianglededucepolygon

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Angle sums in triangles and polygons

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

In a nutshell

Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Triangles first

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

3

Explore the idea

Part 3 of 14

Learn

Triangles first

The angles in any triangle always sum to 180°. This can be shown by tearing the three corners off a paper triangle and placing them together to form a straight line.

4

Explore the idea

Part 4 of 14

Learn

Worked example: polygon sum

A polygon can be split into (n-2) triangles, where n is the number of sides. For a hexagon, n = 6, so it splits into 4 triangles: angle sum = 4 × 180° = 720°.

5

Quick check

Part 5 of 14

Quick check

What do the angles in a triangle always sum to?

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

What is the angle sum of a hexagon (6 sides)?

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Worked example: missing angle

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

9

Explore the idea

Part 9 of 14

Learn

Worked example: missing angle

A quadrilateral has three angles of 90°, 85° and 100°. Since the sum is 360°, the fourth angle = 360 - (90+85+100) = 360 - 275 = 85°.

10

Quick check

Part 10 of 14

Quick check

A quadrilateral has angles 90°, 85° and 100°. What is the fourth angle?

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.

The ____ in any triangle always sum to 180°.

This can be shown by tearing the three corners off a paper ____ and placing them together to form a straight line.

A ____ can be split into (n-2) triangles, where n is the number of sides.

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Angle sums in triangles and polygons

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

  1. 1. What do the angles in a triangle always sum to?

  2. 2. What is the angle sum of a hexagon (6 sides)?

  3. 3. A quadrilateral has angles 90°, 85° and 100°. What is the fourth angle?

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

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Points this lesson

0

Best run

0 in a row

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

Ask Luna

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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    Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

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