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      Exterior angles of polygons

      Lesson details

      Learning outcome

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

      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.

      Teacher tip

      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.

      Licence

      This content is © Oak National Academy Limited (2025), 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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      Prior knowledge starter quiz

      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

      To help you plan your 8 maths lesson on: Exterior angles of polygons, download all teaching resources for free and adapt to suit your pupils' needs...