Chapter 8: Triangles and polygons
Every polygon angle sum can be derived by dividing the shape into triangles.
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
- • Triangle sum
- • Polygon formula
- • Regular polygons
This lesson at a glance
- 30 minutes
- 17 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Visual introductionPicture this
Chapter 8: Triangles and polygons
Every polygon angle sum can be derived by dividing the shape into triangles.
In a nutshell
Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · Triangle sum
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
Triangle sum
The interior angles of a triangle total 180°. Exterior angles of any polygon total 360° when one is taken at each vertex.
Reset break
Part 4 of 17
Pause
That's sitting 1 of 4 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.
Explore the idea
Part 5 of 17
Learn
Polygon formula
An n-sided polygon divides into n−2 triangles from one vertex, so its interior angle sum is (n−2)×180°. A hexagon totals 720°.
Quick check
Part 6 of 17
Quick check
Part 7 of 17
Reset break
Part 8 of 17
Pause
That's sitting 2 of 4 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.
Learning cycle
Part 9 of 17
Learning cycle 2 of 2
Part 2 · Regular polygons
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Regular polygons
In a regular polygon all interior angles are equal, so divide the total by n. A regular hexagon has interior angle 720÷6=120°.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
Pause
That's sitting 3 of 4 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.
Challenge round
Part 13 of 17
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
Challenge round
Part 14 of 17
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
The interior ____ of a triangle total 180°.
Exterior angles of any ____ total 360° when one is taken at each vertex.
Challenge round
Part 15 of 17
Game · Recall cards
What is the interior angle sum of a pentagon?
Card 1 of 4
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Chapter 8: Triangles and polygons
4 questions, marked with the reasoning shown. No timer.
1. What is the interior angle sum of a pentagon?
2. A triangle has angles 48° and 67°. Find the third.
3. Each interior angle of a regular hexagon is:
4. What do the angles in a triangle always sum to?
Lesson round-up
Part 17 of 17
Lesson round-up
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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