New
New
Year 8

Exterior angles of polygons

I can find the sum of the exterior angles of a polygon.

New
New
Year 8

Exterior angles of polygons

I can find the sum of the exterior angles of a polygon.

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Lesson details

Key learning points

  1. The sum of the exterior angles of a polygon can be demonstrated using a point.
  2. The sum of the exterior angles of a polygon can be proven using interior angles and the angles on a straight line.
  3. The angle sum of a triangle can also be proven using exterior angles .
  4. The size of the exterior angle of any polygon can be found using the sum of angles.

Keywords

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

  • Exterior angle - an angle on the outside of a polygon between an extension of an edge and its adjacent edge.

  • Supplementary angle - a pair of angles that sum to 180°.

Common misconception

The exterior angle is the entire reflex angle that is on the outside of each vertex of a shape.

Ask a pupil to stand and walk around the room to trace a shape. The angle that the pupil turns at each vertex is an exterior angle.

Some slides contain links to GeoGebra activities which are similar to those on the slides. If pupils have access to web browsers, they could attempt the activities themselves before working through the slides as a class.
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 on the outside of a polygon between an extension of an edge and its adjacent edge.
acute
alternate
Correct answer: exterior
interior
obtuse
Q2.
Adjacent angles on a straight line sum to °.
Correct Answer: 180, one hundred and eighty, 180°, one hundred and eighty degrees
Q3.
The angle $$x$$° is °.
An image in a quiz
Correct Answer: 70, 70°, seventy, seventy degrees
Q4.
What is the size of ∠CDA?
An image in a quiz
73°
84°
Correct answer: 95°
108°
Q5.
A heptagon is a 7-sided polygon. The sum of its interior angles is °.
Correct Answer: 900, 900°, nine hundred
Q6.
Solve the equation: $$5x + 40 = 360$$. $$x = $$
Correct Answer: 64, sixty four, x=64, x = 64

6 Questions

Q1.
An interior angle and its adjacent exterior angle sum to °.
Correct Answer: 180, one hundred and eighty, 180°
Q2.
In which diagram is an exterior angle marked?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q3.
The exterior angle at B is °.
An image in a quiz
Correct Answer: 131, one hundred and thirty one, 131°
Q4.
Exterior angles in a polygon sum to °.
Correct Answer: 360, three hundred and sixty, 360°
Q5.
The angle $$x$$° is °.
An image in a quiz
Correct Answer: 117, one hundred and seventeen, 117°
Q6.
The value of $$x$$ is .
An image in a quiz
Correct Answer: 96, ninety six, 96°, x=96, x = 96