Internal and external

Find missing interior and exterior angles of triangles and polygons using the angle sum formula (n-2) x 180 degrees, the linear-pair relationship between an interior angle and its adjacent exterior angle (they sum to 180 degrees), and the fact that the exterior angles of any polygon always sum to 360 degrees; apply these both forwards (find an angle) and backwards (find the number of sides of a regular polygon from a given angle).

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM5-5
New NZC (2026)
  • NZC26-P4-GEO-SHP-P-Y10-01

Resources

Terminology

  • Interior angle
  • Exterior angle
  • Regular polygon
  • Irregular polygon
  • Linear pair

Task goals

  • Calculate the sum of the interior angles of any polygon using $(n-2) \times 180°$.
  • Calculate the sum of the exterior angles of any polygon, and recall that it is always $360°$.
  • Find the size of each interior angle of a regular polygon.
  • Find the size of each exterior angle of a regular polygon.
  • Use a known interior or exterior angle to find the number of sides of a regular polygon.
  • Use the fact that an interior angle and its exterior angle form a linear pair (sum to $180°$) to find a missing angle.

Where this fits

What leads into this objective, and where it goes next.

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