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      Problem solving with polygons

      Lesson details

      Learning outcome

      I can use my knowledge of polygons to solve problems.

      Key learning points

      1. Problems can be solved using parallel line angle facts.
      2. Problems can be solved using interior and exterior angles of polygons.
      3. Problems can be solved and the solution justified using angle facts.
      4. It is possible to write algebraic statements about connected angles.
      5. Your knowledge of algebraic manipulation may be useful.

      Keywords

      • Corresponding angles - Corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.

      • Alternate angles - A pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

      • Co-interior angles - Co-interior angles are on the same side of the transversal line and in between the two other lines.

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

      • Exterior angles - 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 might not know how to start an angle problem if they focus too much on the final solution.

      You can start an angle problem by working out any angle on the diagram. The more angles you work out, the easier the final solution becomes.

      Teacher tip

      If pupils have tracing paper, they could use it to help them solve problems with intersecting polygons by tracing each polygon onto a different sheet. They could also use the tracings to explore what other problems can be made by intersecting polygons.

      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.
      Match each pair of angles with the keywords that describe the relationship between them.

      An image in a quiz
      Correct Answer:∠BCD and ∠CEF,corresponding angles

      corresponding angles

      Correct Answer:∠ACE and ∠HEC,co-interior angles

      co-interior angles

      Correct Answer:∠ACE and ∠CEF,alternate angles

      alternate angles

      Correct Answer:∠HEC and ∠GEF,vertically opposite angles

      vertically opposite angles

      Q2.
      A dodecagon has 12 sides. Find the sum of the interior angles in a dodecagon.

      180°
      360°
      Correct answer: 1800°
      2160°
      2520°

      Q3.
      Exterior angles for any polygon sum to °.

      Correct Answer: 360, three hundred and sixty, 360°

      Q4.
      Each exterior angle for a regular hexagon is °.

      Correct Answer: 60, sixty, 60°

      Q5.
      Each interior angle in a regular octagon is °.

      Correct Answer: 135, one hundred and thirty five, 135°

      Q6.
      The pentagon and hexagon in the diagram are both regular. The angle marked in the diagram is °.

      An image in a quiz
      Correct Answer: 132, one hundred and thirty two, 132°

      6 Questions

      Q1.
      Angles on the same side of the transversal line and in between the two other lines are called angles.

      alternate
      Correct answer: co-interior
      corresponding
      vertically opposite

      Q2.
      Which algebraic statement correctly expresses $$y$$ in terms of $$x$$?

      An image in a quiz
      $$y=x$$
      $$y= {x\over2}$$
      Correct answer: $$y=180-x$$
      $$y=360-x$$

      Q3.
      Which algebraic statement correctly expresses $$y$$ in terms of $$x$$?

      An image in a quiz
      $$y=2x$$
      $$y=270-x$$
      Correct answer: $$y=270-2x$$
      $$y=360-x$$
      $$y=360-2x$$

      Q4.
      In which diagram is $$y=180-x$$?

      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

      Q5.
      The size of the angle marked in the diagram is °.

      An image in a quiz
      Correct Answer: 30, thirty, 30°

      Q6.
      The size of the angle marked in the diagram is °.

      An image in a quiz
      Correct Answer: 60, sixty, 60°

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