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Year 8

Deriving the sum of interior angles in multiple ways

I can use reasoning to derive the sum of interior angles in multiple ways.

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New
New
Year 8

Deriving the sum of interior angles in multiple ways

I can use reasoning to derive the sum of interior angles in multiple ways.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Not all vertices of component shapes contribute to the sum of the interior angles of a composite shape.
  2. A numerical sequence can be used to derive the sum of interior angles.
  3. A formula can be derived to find the sum of interior angles.

Common misconception

Interior angles always sum to 180 times the number of component triangles it is split into.

If line segments drawn make new vertices in the polygon, its angles won't contribute to the sum of interior angles in the initial polygon.

Keywords

  • Polygon - A polygon is a flat (2D), closed figure made up of straight line segments.

  • Interior angle - An interior angle is an angle formed inside a polygon by two of its edges.

  • Sum - The sum is the total when numbers are added together.

Following Task A, pupils could explore their own methods for splitting up a polygon into triangles and calculating the sum of interior angles.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
A is a flat (2D), closed figure made up of straight line segments.
Correct Answer: polygon
Q2.
What is the size of ∠BCD?
An image in a quiz
Correct answer: 73°
84°
95°
108°
Q3.
A hendecagon has 11 sides. The minimum number of triangles that it could be split into is .
Correct Answer: 9, nine
Q4.
A hexadecagon has 16 sides. Which calculation would find the sum of its interior angles?
Correct answer: $$14 \times 180$$
$$14 \times 360$$
$$16 \times 180$$
$$16 \times 360$$
Q5.
Angles around a point sum to °.
Correct Answer: 360, three hundred and sixty, 360°
Q6.
Evaluate the expression $$20(x − 2)$$ when $$x=5$$.
Correct Answer: 60, sixty

Exit quiz

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6 Questions

Q1.
Each time the number of sides of a polygon increases by 1, the sum of the interior angles increases by °.
Correct Answer: 180, 180°, one hundred and eighty
Q2.
The interior angles in 19-sided polygon sum to 3060°. Therefore the interior angles in a 20-sided polygon sum to °.
Correct Answer: 3240, 3240°, 3 240, 3,240
Q3.
Which expression can be used to calculate the sum of interior angles in a polygon by substituting $$n$$ for the number of sides?
$$180n$$
$$180n - 2$$
Correct answer: $$180(n - 2)$$
$$180n + 2$$
$$180(n + 2)$$
Q4.
A triacontagon is a polygon with 30 sides. Which calculation finds the sum of its interior angles?
$$180 \times 30$$
Correct answer: $$180 \times (30 - 2)$$
$$180 \times (30 + 2)$$
Q5.
A tetracontagon is a polygon with 40 sides. Its interior angles sum to °.
Correct Answer: 6840, 6840°, 6,840, 6 840
Q6.
A polygon has interior angles which sum to 720°. The polygon has sides.
Correct Answer: 6, six