New
New
Year 8

Interior angles of a polygon

I can find the interior angle of any polygon.

New
New
Year 8

Interior angles of a polygon

I can find the interior angle of any polygon.

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Lesson details

Key learning points

  1. Any polygon can be split into triangles.
  2. Using these triangles you can demonstrate the rule for the interior angle sum of a polygon.
  3. A missing interior angle in any polygon can be found.

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.

Common misconception

When splitting a polygon into triangles, pupils may draw line segments that cross inside the shape.

By choosing a single common vertex for all the triangles, the line segments will not cross inside the shape.

There are often many different ways of approaching a question. Encourage pupils to use words to explain their steps. Checking the angles all add up at the end can be a useful self-checking technique once all angles in a polygon are found.
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).

Lesson video

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6 Questions

Q1.
An angle is an angle formed inside a polygon by two of its edges.
acute
alternate
exterior
Correct answer: interior
obtuse
Q2.
The interior angles of a triangle sum to °.
Correct Answer: 180, one hundred and eighty
Q3.
What is the size of ∠ABC?
An image in a quiz
73°
Correct answer: 84°
95°
108°
Q4.
What is the value of $$x$$? $$x=$$ .
An image in a quiz
Correct Answer: 49, forty-nine, 49 degrees, 49°, forty-nine degrees
Q5.
Starting with the smallest, sort the angles in ascending order of size.
1 - acute
2 - right angle
3 - obtuse
4 - reflex
Q6.
What is the size of the angle $$x$$°?
An image in a quiz
Correct answer: 52°
58°
64°

6 Questions

Q1.
A pentadecagon has 15 sides. The minimum number of triangles that it could be split into is .
Correct Answer: 13, thirteen
Q2.
An octadecagon has 18 sides. Which calculation would find the sum of its interior angles?
Correct answer: $$16 \times 180$$
$$18 \times 180$$
$$20 \times 180$$
Q3.
The interior angles in the hexagon sum to °.
An image in a quiz
Correct Answer: 720, 720°
Q4.
The interior angles of a pentagon sum to °.
Correct Answer: 540, five hundred and forty, 540°, five hundred and forty degrees
Q5.
The size of the angle $$x$$° is °.
An image in a quiz
Correct Answer: 141, one hundred and forty one, 141°, x=141, x = 141
Q6.
The size of the angle $$x$$° is °.
An image in a quiz
Correct Answer: 112, one hundred and twelve, 112°, x=112, x = 112