Basic angle rules

Apply the four core angle rules — angles on a straight line, angles around a point, vertically opposite angles, and the triangle angle sum — to find missing angles.

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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-Y9-02

Resources

Terminology

  • angles on a straight line
  • angles around a point
  • vertically opposite angles
  • full revolution
  • triangle angle sum
  • scalene triangle
  • isosceles triangle
  • equilateral triangle

Task goals

  • Calculate a missing angle on a straight line using the fact that angles on a line sum to 180 degrees.
  • Calculate a missing angle around a point using the fact that angles around a point sum to 360 degrees.
  • Identify vertically opposite angles formed by two intersecting lines and explain why they are equal.
  • Find a missing angle in a triangle given the other two, using the fact that angles in a triangle sum to 180 degrees.
  • Combine two or more of these rules to solve multi-step angle problems, including problems that use algebraic expressions or ratios.

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Basic angle rules

Basic angle rules

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