Angles in Polygons

Use the interior angle sum formula (n-2)\times180^\circ to find the total interior angle sum of a named polygon and calculate one missing interior 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-K-Y9-02

Resources

Terminology

  • Interior angle
  • Exterior angle
  • Regular polygon
  • Irregular polygon
  • Angle sum

Task goals

  • Use the interior angle sum formula (n-2) x 180 degrees to find the total interior angle sum of a named polygon and calculate one missing interior angle.
  • Calculate each interior and exterior angle of a regular polygon.
  • Use the fact that the exterior angles of any polygon sum to 360 degrees to find the number of sides of a regular polygon.
  • Solve multi-step problems combining interior and exterior angle relationships in irregular or composite polygons, justifying each step with the angle property used.

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Angles in Polygons

Angles in Polygons

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