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      Interior and exterior angles of regular polygons

      Lesson details

      Learning outcome

      I can find the interior and exterior angles of regular polygons.

      Key learning points

      1. Exterior angles of a regular polygon are equal.
      2. The size of the exterior angle of a regular polygon can be determined.
      3. Interior angles of regular polygons are equal.
      4. The size of the interior angle of a regular polygon can be determined.
      5. The number of sides in a regular polygon can be determined from the size of the interior or exterior angle.

      Keywords

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

      • Regular polygon - A regular polygon has sides that are equal and interior (inside) angles that are all equal.

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

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

      Common misconception

      Pupils may solve angle problems by using methods which are less efficient than others.

      While less efficient methods are fine, encourage pupils to review their work each time they solve a problem to consider alternative methods.

      Teacher tip

      One of the slides contains a link to a GeoGebra activity similar to what Sofia uses. If pupils have access to web browsers, they could use it to perform a similar investigation by attempting to draw regular polygons using different exterior angles.

      Licence

      This content is © Oak National Academy Limited (2026), 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.
      A polygon has sides that are equal and interior (inside) angles that are all equal.

      Correct Answer: regular

      Q2.
      What is the size of ∠DAB?

      An image in a quiz
      73°
      84°
      95°
      Correct answer: 108°

      Q3.
      Which image shows a regular pentagon?

      An image in a quiz
      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q4.
      Starting with the smallest, sort the shapes in ascending order according to their perimeters.

      1 - a regular hexagon with a side length of 3 cm
      2 - a regular decagon with a side length of 2 cm
      3 - a regular pentagon with a side length of 6 cm
      4 - a regular octagon with a side length of 5 cm

      Q5.
      Find the value of $$x$$.

      An image in a quiz
      Correct Answer: 108, 108°, x=108, x = 108, one hundred and eight

      Q6.
      Find the value of $$x$$.

      An image in a quiz
      Correct Answer: 100, one hundred, 100°, x=100, x = 100

      6 Questions

      Q1.
      Each exterior angle in a regular hexagon is °.

      Correct Answer: 60, 60°, sixty, sixty degrees

      Q2.
      Each interior angle in a regular pentagon is °.

      Correct Answer: 108, 108°

      Q3.
      Is it possible for a decagon to be regular if one of its exterior angles is 30°?

      Correct answer: no
      yes
      sometimes

      Q4.
      Is it possible for an octagon to be regular if one of its interior angles is 45°?

      Correct answer: no
      yes
      sometimes

      Q5.
      Which calculations can be used to find the size of the shaded angle?

      An image in a quiz
      $$108 + 90$$
      Correct answer: $$108 - 90$$
      $$90 + 72$$
      Correct answer: $$90 - 72$$
      $$(90 + 72) \div 2$$

      Q6.
      The size of the shaded angle is °.

      An image in a quiz
      Correct Answer: 150, one hundred and fifty, a hundred and fifty, 150°

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